   Chapter 2.7, Problem 60E

Chapter
Section
Textbook Problem

Determine whether f'(0) exists. f ( x ) = { x 2 sin 1 x   if   x ≠ 0 0       if   x = 0

To determine

Whether f(0) exits or not.

Explanation

Squeeze theorem:

Suppose an inequality of functions g(x)f(x)h(x) in a interval around c and that limxcg(x)=L=limxch(x). Then limxcf(x)=L.

Definition:

A function f(x) is differentiable at point x, then f'(x)=limh0f(x+h)f(x)h.

Calculation:

Consider the function f(x)=x2sin(1x) when x0 and f(0)=0,

By definition, f'(x)=limh0f(x+h)f(x)h

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

let f(x) = x3 + 5, g(x) = x2 2, and h(x)= 2x + 4. Find the rule for each function. 2. f g

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Find f. f(x) = 8x3 + 5, f(1) = 0, f(1) = 8

Single Variable Calculus: Early Transcendentals, Volume I

Define the terms population and sample, and explain the role of each in a research study.

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate in problems 1-4. Write all the answers without using exponents. 2. (a) ...

Mathematical Applications for the Management, Life, and Social Sciences

True or False: f(x) = tan x is differentiable at x=2.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 