   Chapter 2.2, Problem 30E ### 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) Estimate the value of lim x → 0 sin x sin π x by graphing the function f(x) = (sin x)/(sin πx). State your answer correct to two decimal places.(b) Check your answer in part (a) by evaluating f(x) for values of x that approach 0.

(a)

To determine

To estimate: The value of limx0sinxsinπx by graphing the function f(x)=sinxsinπx.

Explanation

Using the graphing calculator, the graph of the function f(x)=sinxsinπx is drawn and shown below in Figure 1.

Zoom the graph towards the point where the graph crosses the y-axis as shown below in Figure 2.

From Figure 2, it is observed that graph of f(x)=sinxsinπx approaches 0.32 as x approaches 0 from either side.

Since the right hand and the left hand limits are equal, the value of limx0sinxsinπx exists

(b)

To determine

To check: The correctness of the answer obtained in part (a) by evaluating the value of f(x)=sinxsinπx as x approaches 0.

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 