   Chapter 2.4, Problem 44E ### 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

# Suppose that lim x → a f ( x ) = ∞   and  lim x → a g ( x ) = c , where c is a real number. Prove each statement.(a) lim x → a [ f ( x ) + g ( x ) ] = ∞ (b) lim x → a [ f ( x ) g ( x ) ] = ∞   if   c > 0 (c) lim x → a [ f ( x ) g ( x ) ] = − ∞   if   c < 0

(a)

To determine

To prove: The value of the limit of the function limxa[f(x)+g(x)]=

Explanation

Result used:

Sum law:limxa[f(x)+g(x)]=limxa[f(x)]+limxa[g(x)]

Calculation:

Obtain the limit of the function f(x)g(x) as x approaches a.

Suppose limxaf(x)= and limxag(x)=c where c is a real number.

Consider limxa[f(x)+g(x)]

(b)

To determine

To prove: The value of the limit of the function limxa[f(x)g(x)]= if c>0.

(c)

To determine

To prove: The value of the limit of the function limxa[f(x)g(x)]= if c<0.

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