BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2, Problem 16RQ
To determine

To find: Whether the statement “If f(r) exists then limxrf(x)=f(r) ” is true.

Expert Solution

Answer to Problem 16RQ

The statement “I If f(r) exists then limxrf(x)=f(r) ” is true

Explanation of Solution

Given information:

The given statement is “ f(r) exists”

Calculation:

Since f(r) exists, consider xr .

  f(x)f(r)=f(x)f(r)xr(xr))

Take limit both the sides.

  limxrf(x)f(r)=limxrf(x)f(r)xr×limxr(xr))limxrf(x)f(r)=f(r)(rr)limxrf(x)f(r)=0

Further solve.

  limxrf(x)=limxrf(r)=f(r)

Therefore, the statement “If f(r) exists then limxrf(x)=f(r) ” is true

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!