Please help! Thank you. f(x + h) – f(x)Use the definition of a derivative f' (x) = limto show if f' (0)does exist or%3Dh→0hf' (0) does not exist.f(x) = {"{2²sin(÷)x + 0x = 01. Use definition and show steps to get f' (0) = lim h-sin(G)h→02. Use squeeze theorem to evaluate limit and show the steps.3. Make a decision on f'(0)does exist or f' (0) does not exist.

Name: Please help! Thank you. f(x + h) – f(x)Use the definition of a derivat
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Description: Please help! Thank you. f(x + h) – f(x)Use the definition of a derivative f' (x) = limto show if f' (0)does exist or%3Dh→0hf' (0) does not exist.f(x) = {"{2²sin(÷)x + 0x = 01. Use definition and show steps to get f' (0) = lim h-sin(G)h→02. Use squeez

Given function is : fx=x2sin4x , x≠00 , x=0 Squeeze theorem: If xn≤yn≤zn for all…

Answered: f(x +h) – f(æ) Use the definition of a…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Please help! Thank you.

f(x + h) – f(x)
Use the definition of a derivative f' (x) = lim
to show if f' (0)does exist or
%3D
h→0
h
f' (0) does not exist.
f(x) = {"
{2²sin(÷)
x + 0
x = 0
1. Use definition and show steps to get f' (0) = lim h-sin(G)
h→0
2. Use squeeze theorem to evaluate limit and show the steps.
3. Make a decision on f'(0)does exist or f' (0) does not exist.

Expert Solution

Step 1

Given function is :

$f (x) = \{\begin{cases} x^{2} \sin (\frac{4}{x}), x \neq 0 \\ 0, x = 0 \end{cases}$

Squeeze theorem:

If $x_{n} \leq y_{n} \leq z_{n} for all n \in ℕ$ , and $\lim_{} x_{n} = \lim_{} z_{n}$ . Then $\lim_{} x_{n} = \lim_{} y_{n} = \lim_{} z_{n}$ .

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