   Chapter 2, Problem 5P ### 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

# Evaluate the following limits, if they exist, where 〚 x 〛 denotes the greatest integer function.(a) lim x → 0 〚 x 〛 x (b) lim x → 0 x 〚 1 / x 〛

(a)

To determine

To evaluate: The limit of the function limx0xx.

Explanation

Definition used:

Greatest integer function:x= the largest integer that is less than or equal to x.

Calculation:

Obtain the limit of the function limx0xx.

Let the function f(x)=xx.

For 0<x<1,

By the definition of greatest integer function, x=0.

Thus, xx=0. (1)

For 1<x<0,

By the definition of greatest integer function, x=1.

Thus, xx=1x. (2)

The left hand limit of the function as x approaches 0 is computed as follows,

limx0f(x)=limx0xx=limx0(1x)

(b)

To determine

To evaluate: The limit of the function limx0x1x.

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