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Chapter 1: Q. 25 (page 153)

Limits of combinations: Fill in the blanks to complete the limit

rules that follow. You may assume that k and c are any real

numbers and that both limx→cf(x)andlimx→cg(x)exist.

limx→cf(x)g(x)=______,providedthat_____

Short Answer

Expert verified

The value of the limit islimx→cf(x)g(x)=limx→cf(x)limx→cg(x),providedthatlimx→cg(x)≠0.

Step by step solution

01

Step 1. Given Information. 

The given limit function islimx→cf(x)g(x).

02

Step 2. Filling the blank.

To fill the blank, use the Quotient Rule of limits.

So,

limx→cf(x)g(x)=limx→cf(x)limx→cg(x),providedthatlimx→cg(x)≠0.

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