# The value of lim x → 1 x 1000 − 1 x − 1 . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 3.1, Problem 71E
To determine

## To find: The value of limx→1x1000−1x−1.

Expert Solution

The value of limx1x10001x1 is 1000.

### Explanation of Solution

Derivative rules:

Power rule: ddx(xn)=nxn1

Calculation:

Note that f(x) is differentiable at x=a if f(a)=limxaf(x)f(a)xa exist. (1)

Re-write the given limit as,

limx1x10001x1=limx1x100011000x1          [11000=1]=f(1)

Where, f(x)=x1000.

Obtain the value of f(1).

The derivative of the function f(x)=x1000 is, f(x)=ddx(x1000).

Apply the power rule and simplify the expression as,

f(x)=1000x10001=1000x999

Substitute x=1 in the expression for f(x).

f(1)=1000(1)999=1000

Therefore, the value of limx1x10001x1=1000.

### 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!