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 3.1, Problem 71E
To determine

To find: The value of limx1x10001x1.

Expert Solution

Answer to Problem 71E

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.

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