Estimate the Limit by Graphing the Function for an Appropriate

question 86

Essay

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.
$\begin{aligned}\lim _{ x \rightarrow \infty } \frac { \sin ( 1 / x ) } { e ^ { 1 / x } } = & \lim _{ x \rightarrow \infty } \frac { - x ^ { - 2 } \cos ( 1 / x ) } { - x ^ { - 2 } e ^ { 1 / x } } \\& = \lim _ { x \rightarrow \infty } \frac { \cos ( 1 / x ) } { e ^ { 1 / x } } = \frac { 1 } { 1 } = 1\end{aligned}$

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Definitions:

Confidence Interval

A spectrum of numbers obtained from sample observations which is expected to include the value of an unidentified population parameter, given a certain confidence degree.

Confidence Interval

A range of values within which there is a specified probability that the true parameter value lies.

Population Standard Error

A measure that estimates the variability or dispersion of a population parameter based on a sample.

Mean

The average of a set of numbers, calculated by adding all the values together and dividing by the number of values.