![[Graphics:Images/AnalyticFunctionMod_gr_180.gif]](../Images/AnalyticFunctionMod_gr_180.gif){kind=small}
. Extra Example
2. Use L'Hopital's rule to
find .
Explore Extra Example 2.
![[Graphics:../Images/AnalyticFunctionMod_gr_181.gif]](../Images/AnalyticFunctionMod_gr_181.gif)
![[Graphics:../Images/AnalyticFunctionMod_gr_182.gif]](../Images/AnalyticFunctionMod_gr_182.gif){kind=small}
Direct substitution of ![[Graphics:../Images/AnalyticFunctionMod_gr_183.gif]](../Images/AnalyticFunctionMod_gr_183.gif){kind=small}
is
indeterminate.
![[Graphics:../Images/AnalyticFunctionMod_gr_184.gif]](../Images/AnalyticFunctionMod_gr_184.gif)
![[Graphics:../Images/AnalyticFunctionMod_gr_185.gif]](../Images/AnalyticFunctionMod_gr_185.gif){kind=small}
![[Graphics:../Images/AnalyticFunctionMod_gr_186.gif]](../Images/AnalyticFunctionMod_gr_186.gif){kind=small}
![[Graphics:../Images/AnalyticFunctionMod_gr_187.gif]](../Images/AnalyticFunctionMod_gr_187.gif){kind=small}
![[Graphics:../Images/AnalyticFunctionMod_gr_188.gif]](../Images/AnalyticFunctionMod_gr_188.gif){kind=small}
Find the limit as ![[Graphics:../Images/AnalyticFunctionMod_gr_189.gif]](../Images/AnalyticFunctionMod_gr_189.gif){kind=small}
.
![[Graphics:../Images/AnalyticFunctionMod_gr_190.gif]](../Images/AnalyticFunctionMod_gr_190.gif)
![[Graphics:../Images/AnalyticFunctionMod_gr_191.gif]](../Images/AnalyticFunctionMod_gr_191.gif)
Which agrees with the L'Hopital rule computation.
![[Graphics:../Images/AnalyticFunctionMod_gr_192.gif]](../Images/AnalyticFunctionMod_gr_192.gif)
![[Graphics:../Images/AnalyticFunctionMod_gr_193.gif]](../Images/AnalyticFunctionMod_gr_193.gif)
Which agrees with evaluation of the quotient ![[Graphics:../Images/AnalyticFunctionMod_gr_194.gif]](../Images/AnalyticFunctionMod_gr_194.gif){kind=small}
.
![[Graphics:../Images/AnalyticFunctionMod_gr_195.gif]](../Images/AnalyticFunctionMod_gr_195.gif)
![[Graphics:../Images/AnalyticFunctionMod_gr_196.gif]](../Images/AnalyticFunctionMod_gr_196.gif)