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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

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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