   Chapter 2, Problem 54RE ### 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

# Let f ( x ) = 〚 x 〛 + 〚 − x 〛 . (a) For what values of a does lim x → a f ( x ) exist?(b) At what numbers is f discontinuous?

(a)

To determine

To find: The values of a for which limxaf(x) exists.

Explanation

Given:

f(x)=x+x

Calculation:

Simplify the function f(x)=x+x as follows.

f(x)=x+x=x+x=(x)+(x)=f(x)

Recall that a function is even if f(x)=f(x).

Thus f(x) is an even function.

Since f(x)=f(x), check for only x0

When x is an integer, x is also an integer

(b)

To determine

To find: The numbers where f is discontinuous.

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