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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
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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