   Chapter 2.6, Problem 65E ### 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

# (a) Use the Squeeze Theorem to evaluate lim x → ∞ sin x x . (b) Graph .f(x) = (sin x)/x. How many times does the graph cross the asymptote?

(a)

To determine

To evaluate: The value of limxsinxx by using the squeeze theorem.

Explanation

Theorem 1: The Squeeze Theorem

“If f(x)g(x)h(x) when x is near a (except possibly at a) and limxaf(x)=limxah(x)=L then limxag(x)=L.”

Theorem 2: If r>0 is a rational number, then limx1xr=0.

Calculation:

The trigonometric sine function varies from -1 to 1.

That is, 1sinx1

(b)

To determine

To find: The graph of the function crosses the asymptote.

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