   Chapter 2.6, Problem 36E ### 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

# Find the limit or show that it does not exist. lim x → ∞ e 3 x − e − 3 x e 3 x + e − 3 x

To determine

To find: The value of limxe3xe3xe3x+e3x.

Explanation

Limit Laws used: Suppose that c is a constant and the limits limxaf(x) and limxag(x) exists, then

Limit law 1: limxa[f(x)+g(x)]=limxaf(x)+limxag(x)

Limit law 2:limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 3:limxa[cf(x)]=climxaf(x)

Limit law 4:limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 5:limxaf(x)g(x)=limxaf(x)limxag(x) if limxag(x)0

Limit law 6:limxa[f(x)]n=[limxaf(x)]n where n is a positive integer.

Limit law 7:limxac=c

Calculation:

Obtain the value of the function as x approaches infinity.

Consider the function, f(x)e3xe3xe3x+e3x.

Divide both the numerator and the denominator by the highest power of ex in the denominator. That is, e3x0.

f(x)=e3xe3xe3xe3x+e3xe3x=e3xe3xe3xe3xe3xe3x+e3xe3x=11e3xe3x1+1e3xe3x=11e6x1+1e6x

Take the limit of f(x) as x approaches infinity

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