   Chapter 4.5, Problem 76E ### 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

# Use the asymptotic behavior of f(x) = sin x + e−x to sketch its graph without going through the curve-sketching procedure of this section.

To determine

To Sketch: the curve using the asymptotic behavior of function f(x)=sinx+ex .

Explanation

Given:

The equation of the curve is as below.

f(x)=sinx+ex (1)

Calculation:

D)

Compute the asymptote.

Apply the expression limx[f(x)] to the function.

limx[f(x)]=limx[sin+e]=limx[sin+1e]=limx[sin+0]=

The function will not have a fixed value, as it can have any number between the range (1,1) . There is no horizontal asymptote.

The function sinx+ex does not become infinity for any value of x, and there will be no vertical asymptote.

Sketch the curve.

Compute the value of y .

Substitute the value of 1 for x in equation (1).

f(1)=sin(1)+e1f(1)=1.2094

Repeat the calculation and tabulate the values of x and y in the below table to draw the curve.

 x in degrees y x in radians -180 23.14 -3.1416 -170 19.26 -2.9671 -160 15.98 -2.7925 -150 13.21 -2.6180 -140 10.87 -2.4435 -130 8.90 -2.2689 -120 7.25 -2.0944 -110 5.88 -1.9199 -100 4.74 -1.7453 -90 3.81 -1.5708 -80 3.06 -1.3963 -70 2

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Study Guide for Stewart's Multivariable Calculus, 8th 