MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C97CE4.ECB914F0" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1

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------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/master03.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD6wAAAAUAQgAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC2f8A AAAAAACQAQAAAAAAQAAiQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACQgAAADIKLgCMACcAAABHcmFwaHMgb2YgTG9nIGFuZCBF eHBvbmVudGlhbCBGdW5jdGlvbnMAHgANABYAFgAWABMACwAVAAwACgAWABYAFgAKABYAFgAWAAoA GgASABYAFgAWABYAFgALAAgAFgAJAAsAFwAWABYAEwALAAkAFQAWABMABAAAAC4BAAAcAAAA+wIQ AAcAAAAAALwCAAAAAAECAiJTeXN0ZW0AAAAAAAAYAAAAaGkTAAEAAADkBAAAAAAAAAQAAAAtAQQA BAAAAPABAwADAAAAAAA= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Graph= s of Log and Exponential Functions <= /div>
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Graph= s of Log and Exponential Functions <= /div>
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0080.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0080_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
We gather the following information:
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0081_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0082.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
We gather the following information:
* The domain, find the asymptotes, if any.
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0082_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
We gather the following information:
* The domain, find the asymptotes, if any.
* The x intercept and y intercept
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0083_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0084.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
We gather the following information:
* The domain, find the asymptotes, if any.
* The x intercept and y intercept
* The behavior as x à ± and as x = à asymptotes
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0084_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0085.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
We gather the following information:
* The domain, find the asymptotes, if any.
* The x intercept and y intercept
* The critical points where f ' =3D 0 or f ' is not defined
* The behavior as x à ± and as x = à asymptotes
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0085_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0086.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
We gather the following information:
* The domain, find the asymptotes, if any.
* The x intercept and y intercept
* The critical points where f ' =3D 0 or f ' is not defined
* The inflection points
* The behavior as x à ± and as x = à asymptotes
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0086_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
We gather the following information:
* The domain, find the asymptotes, if any.
* The x intercept and y intercept
* The critical points where f ' =3D 0 or f ' is not defined
* The inflection points
Domain: All real numbers
* The behavior as x à ± and as x = à asymptotes
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0087_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
In this section we examine the graphs of functions
related to log and exponential functions. =
Example: Sketch the graph y =3D     . Find the critical
points and the reflection point, if= any.
Graph= s of Log and Exponential Functions <= /div>
ex
x
We gather the following information:
* The domain, find the asymptotes, if any.
* The x intercept and y intercept
* The critical points where f ' =3D 0 or f ' is not defined
* The inflection points
Domain: All real numbers
* The behavior as x à ± and as x = à asymptotes
x intercept and y intercept: (0, 0)
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0088_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Graph= s of Log and Exponential Functions <= /div>
The behavior as x à ±: =
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The behavior as x à ±: =
xà∞ <= /div>
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0089_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0090_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0090_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0090_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0091_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0091_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0091_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0092_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0092_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0092_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0092_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0093.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
0+
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0093_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0093_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0093_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0093_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0093_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0094.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0094_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0094_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0094_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0094_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0094_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0095.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0095_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0095_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0095_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0095_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0095_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0096.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
=3D
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0096_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0096_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0096_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0096_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0096_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0096_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABC AAEAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0097.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
e2x
ex(1 – x)
=3D
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0097_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0097_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0097_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0097_image045.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0097_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0097_image047.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABC AAEAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0097_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABD AAEAgAAAAAAAAAIHjI+py+0fCgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0098.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
e2x
ex(1 – x)
=3D
e-x(1 – x) = =3D 0 
=3D
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0098_image049.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0098_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0098_image051.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0098_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0098_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0098_image054.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABC AAEAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0098_image055.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABD AAEAgAAAAAAAAAIHjI+py+0fCgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0099.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
e2x
ex(1 – x)
=3D
e-x(1 – x) = =3D 0 when x =3D 1. = ;
=3D
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0099_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0099_image057.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0099_image058.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0099_image059.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0099_image060.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0099_image061.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABC AAEAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0099_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABD AAEAgAAAAAAAAAIHjI+py+0fCgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0100.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The inflection point:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
e2x
ex(1 – x)
=3D
e-x(1 – x) = =3D 0 when x =3D 1. = ;
=3D
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0100_image063.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0100_image064.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0100_image065.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0100_image066.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0100_image067.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0100_image068.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABC AAEAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0100_image069.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABD AAEAgAAAAAAAAAIHjI+py+0fCgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0101.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The inflection point:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
e2x
ex(1 – x)
=3D
e-x(1 – x) = =3D 0 when x =3D 1. = ;
=3D
f " =3D -e-x(1 – x) – e-x <= span style=3D'font-size:156%;color:#006600'> 
------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0101_image070.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0101_image071.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAF ABEAgAAAAAAAAAIRBGIWeKsLoUqHspluzbbzjxUAOx== ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0101_image072.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0101_image073.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AAEAgAAAAAAAAAIEjI+pVgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0101_image074.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAcAgAAAAAAAAAIVjAOpy913nJwKGhaptFB77k1dKDIFADs= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0101_image075.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABC AAEAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0101_image076.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABD AAEAgAAAAAAAAAIHjI+py+0fCgA7 ------=_NextPart_01C97CE4.ECB914F0 Content-Location: file:///C:/4D764A33/10GraphsofLogandExpFunctions_files/slide0102.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The inflection point:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
e2x
ex(1 – x)
=3D
e-x(1 – x) = =3D 0 when x =3D 1. = ;
=3D
f " =3D -e-x(1 – x) – e-x <= span style=3D'font-size:156%;color:#006600'> =3D -2e-x + xe-x <= /div>
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Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The inflection point:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
e2x
ex(1 – x)
=3D
e-x(1 – x) = =3D 0 when x =3D 1. = ;
=3D
f " =3D -e-x(1 – x) &= #8211; e-x  =3D -2e-x + xe-x
=3D e-x(2 – x)
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Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The inflection point:
The behavior as x à ±: =
xà∞ <= /div>
=3D
L'Hopital's Rule
Lim
ex
1
xà∞ <= /div>
=3D 0+
Lim
ex
x
xà-∞
=3D -∞
0+
 f ' =3D
e2x
ex – xex
e2x
ex(1 – x)
=3D
e-x(1 – x) = =3D 0 when x =3D 1. = ;
=3D
f " =3D -e-x(1 – x) &= #8211; e-x  =3D -2e-x + xe-x
=3D e-x(2 – x) =3D 0 à x =3D 2
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Lim
Graph= s of Log and Exponential Functions <= /div>
ex
x
The critical points where f ' =3D 0 or f ' is not defined:
The inflection point:
The behavior as x à