   Chapter 2, Problem 21RQ ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is continuous at a, then f is differentiable at a.

To determine

Whether the statement, “if f is continuous at a then f is differentiable at a” is true or false.

Explanation

Theorem used: If f is continuous at b and limxag(x)=b, then limxaf(g(x))=f(b).

Theorem used: If f is differentiable at a then limxa+f(x)=L=limxaf(x).

Definition of limit: The limit of the function is defined as limh0f(x+h)f(x)h.

Result used: The limit of the function limx0|x|x=1.

The function f is continuous at a, but not differentiable at a.

Because, the right and left derivatives of a function are not equal.

Example:

Let the function f(x)=|x| is continuous at x=0, but not differentiable at x=0.

Calculation:

The limit of the function is defined as 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

#### Convert the expressions in Exercises 8596 radical form. y7/4

Finite Mathematics and Applied Calculus (MindTap Course List)

#### If m1=m2, which line segments are parallel?

Elementary Geometry For College Students, 7e

#### In Problems 14-19, find the value of each sum. 16.

Mathematical Applications for the Management, Life, and Social Sciences

#### Subtract: (0)(3)

Elementary Technical Mathematics

#### Show that 0x2ex2dx=120ex2dx.

Single Variable Calculus: Early Transcendentals

#### True or False: The slope of a tangent line may be interpreted as average velocity.

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

#### Given: ABCF23 Prove: 13

Elementary Geometry for College Students 