Thanks in advance ### Problem Statement**Note:** This problem has an example student explanation in the Feedback.**(a)** Complete the table below given $ f(x) = \frac{\sin(3x)}{x} $.**Round your answers to six decimal places.**| $ x $ | $-0.1$ | $0.01$ | $-0.001$ | $0.001$ | $0.01$ | $0.1$ ||-----------|----------|----------|------------|----------|---------|---------|| $ f(x) $ | Number | Number | Number | Number | Number | Number |**(b)** Estimate $\lim_{{x \to 0}} \frac{\sin(3x)}{x}$.Enter your answer to the nearest integer.\[\lim_{{x \to 0}} \frac{\sin(3x)}{x} = \boxed{\text{Number}}\]

Answered: Note: This problem has an example…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Thanks in advance

### Problem Statement

**Note:** This problem has an example student explanation in the Feedback.

**(a)** Complete the table below given $ f(x) = \frac{\sin(3x)}{x} $.

**Round your answers to six decimal places.**

| $ x $ | $-0.1$ | $0.01$ | $-0.001$ | $0.001$ | $0.01$ | $0.1$ |
|-----------|----------|----------|------------|----------|---------|---------|
| $ f(x) $ | Number | Number | Number | Number | Number | Number |

**(b)** Estimate $\lim_{{x \to 0}} \frac{\sin(3x)}{x}$.

Enter your answer to the nearest integer.

\[
\lim_{{x \to 0}} \frac{\sin(3x)}{x} = \boxed{\text{Number}}
\]

Expert Solution

Step 1

The limit of the function is a number which the function attains when the variable approaches its

limit from the right and the left.

This means that the limit of a function $f (x)$ is the value L such that $\begin{array}{rcl} \lim_{x \to a^{-}} f (x) & = & L \end{array}$ and $\begin{array}{rcl} \lim_{x \to a^{+}} f (x) & = & L \end{array}$

where $\begin{array}{rcl} \lim_{x \to a^{-}} f (x) \end{array}$ denotes the left hand limit and $\begin{array}{rcl} \lim_{x \to a^{+}} f (x) \end{array}$ denotes the right hand limit of $f (x)$ .