Estimate the limit by graphing the function for an appropriate domain. Confirm your estimate by using L'Hopital's rule.
Show each step of your calculation.
-A student attempted to use l'Hôpital's Rule as follows. Identify the student's error.
$\begin{aligned}
\lim _{ x \rightarrow \infty } \frac { \sin ( 1 / x ) } { e ^ { 1 / x } } = & \lim _{ x \rightarrow \infty } \frac { - x ^ { - 2 } \cos ( 1 / x ) } { - x ^ { - 2 } e ^ { 1 / x } } \
& = \lim _ { x \rightarrow \infty } \frac { \cos ( 1 / x ) } { e ^ { 1 / x } } = \frac { 1 } { 1 } = 1
\end{aligned}$

Question

Estimate the limit by graphing the function for an appropriate domain. Confirm your estimate by using L'Hopital's rule.
Show each step of your calculation.
-A student attempted to use l'Hôpital's Rule as follows. Identify the student's error.
$\begin{aligned}
\lim _{ x \rightarrow \infty } \frac { \sin ( 1 / x ) } { e ^ { 1 / x } } = & \lim _{ x \rightarrow \infty }  \frac { - x ^ { - 2 } \cos ( 1 / x ) } { - x ^ { - 2 } e ^ { 1 / x } } \
& = \lim _ { x \rightarrow \infty } \frac { \cos ( 1 / x ) } { e ^ { 1 / x } } = \frac { 1 } { 1 } = 1
\end{aligned}$

Quizplus · Accepted Answer

The Answer of Estimate the limit by graphing the function for an appropriate domain. Confirm your estimate by using L'Hopital's rule.
Show each step of your calculation.
-A student attempted to use l'Hôpital's Rule as follows. Identify the student's error.
$\begin{aligned}
\lim _{ x \rightarrow \infty } \frac { \sin ( 1 / x ) } { e ^ { 1 / x } } = & \lim _{ x \rightarrow \infty }  \frac { - x ^ { - 2 } \cos ( 1 / x ) } { - x ^ { - 2 } e ^ { 1 / x } } \
& = \lim _ { x \rightarrow \infty } \frac { \cos ( 1 / x ) } { e ^ { 1 / x } } = \frac { 1 } { 1 } = 1
\end{aligned}$

Estimate the Limit by Graphing the Function for an Appropriate