Chapter 1: Q. 26 (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 $\lim_{x \to c} f (x) and \lim_{x \to c} g (x)$ exist.
$\lim_{x \to c} f (g (x)) =__, provided that_$

Short Answer

Expert verified

The value of the limit is $\lim_{x \to c} f (g (x)) = f (\lim_{x \to c} g (x)), provided that f is continuous at \lim_{x \to c} g (x) .$

Step by step solution

Step 1. Given Information.

The given limit function is $\lim_{x \to c} f (g (x)) .$

Step 2. Filling the blank.

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

So,

$\lim_{x \to c} f (g (x)) = f (\lim_{x \to c} g (x)), provided that f is continuous at \lim_{x \to c} g (x) .$

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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 $\lim_{x \to c} f (x) and \lim_{x \to c} g (x)$ exist.
$\lim_{x \to c} f (g (x)) =__, provided that_$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Filling the blank.

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Limits of combinations: Fill in the blanks to complete the limitrules that follow. You may assume that k and c are any realnumbers and that both limx→cf(x)andlimx→cg(x)exist.limx→cf(g(x))=______,providedthat_____

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Filling the blank.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

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 $\lim_{x \to c} f (x) and \lim_{x \to c} g (x)$ exist.
$\lim_{x \to c} f (g (x)) =__, provided that_$