## Problem 4Consider the function $ f(x) = \frac{\cos x - e^x}{x} $.### a. Notice that using direct substitution, $\lim_{x \to 0} \frac{\cos x - e^x}{x} = \frac{0}{0}$. What does this usually indicate?### b. Complete the table (accurate to **five decimal places**) for $ f(x) $.\[\begin{array}{c|c|c|c|c|c}x & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\\hlinef(x) & & & & & & \\\end{array}\]### c. Using the results in the table, what do you think the limit is?\[\lim_{x \to 0} \frac{\cos x - e^x}{x} = \underline{\hspace{3cm}}\]### d. How confident are you that your answer in part c is the correct limit? Briefly explain.

Answered: Consider the function f(x) = - cosx-et…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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## Problem 4

Consider the function $ f(x) = \frac{\cos x - e^x}{x} $.

### a.
Notice that using direct substitution, $\lim_{x \to 0} \frac{\cos x - e^x}{x} = \frac{0}{0}$. What does this usually indicate?

### b.
Complete the table (accurate to **five decimal places**) for $ f(x) $.

\[
\begin{array}{c|c|c|c|c|c}
x & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\
\hline
f(x) & & & & & & \\
\end{array}
\]

### c.
Using the results in the table, what do you think the limit is?

\[
\lim_{x \to 0} \frac{\cos x - e^x}{x} = \underline{\hspace{3cm}}
\]

### d.
How confident are you that your answer in part c is the correct limit? Briefly explain.

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Given function is

$f open parentheses x close parentheses equals fraction numerator cos x minus e to the power of x over denominator x end fraction$

We have to discuss about the limit $limit as x rightwards arrow 0 of fraction numerator cos x minus e to the power of x over denominator x end fraction$