   Chapter 2, Problem 14RQ ### 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

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f has domain [0, ∞) and has no horizontal asymptote, then lim x → ∞ f ( x ) = ∞     lim x → ∞ f ( x ) = − ∞

To determine

Whether the statement, “If f has domain [0,) has no horizontal asymptote, then limxf(x)= or limxf(x)=” is true or false.

Explanation

Reason:

The domain [0,) is the set of non-negative numbers.

Here the function f(x)=sinx has domain [0,), it has no horizontal asymptote and does not approach ±.

Consider 1<sinx<1.

It ranges from -1 to 1.

That is, it will oscillate between -1 and 1 as x

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