Chapter 1: Q. 12 (page 152)

Fill in the blanks to complete each of the following theorem statements:
If $\lim_{x \to c} g (x)$ exists and $f (x)$ is a function that is ? to $g (x)$ for all $x$ sufficiently close to ?, but not necessarily at ? , then ?.

Short Answer

Expert verified

If $\lim_{x \to c} g (x)$ exists and $f (x)$ is a function that is equal to $g$ for all $x$ sufficiently close to $c$ , but not necessarily at $c$ , then $\lim_{x \to c} f (x) = \lim_{x \to c} g (x) .$

Step by step solution

Step 1. Given Information.

The given statement is:

If $\lim_{x \to \infty} g (x)$ exists and $f (x)$ is a function that is equal to ? for all $x$ sufficiently close to ? but not necessarily at ?, then ?

Step 2. Fill the blanks.

According to the Cancellation Theorem for Limits,

If $\lim_{x \to \infty} g (x)$ , and $f$ is a function that is equal to $g$ for all $x$ sufficiently close to $c$ except possibly at $c$ itself, then $\lim_{x \to c} f (x) = \lim_{x \to c} g (x) .$

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Fill in the blanks to complete each of the following theorem statements:
If $\lim_{x \to c} g (x)$ exists and $f (x)$ is a function that is ? to $g (x)$ for all $x$ sufficiently close to ?, but not necessarily at ? , then ?.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Fill the blanks.

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Fill in the blanks to complete each of the following theorem statements:If limx→cg(x)exists and f(x)is a function that is ? to g(x) for all x sufficiently close to ?, but not necessarily at ? , then ?.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Fill the blanks.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Mechanics Maths

Probability and Statistics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following theorem statements:
If $\lim_{x \to c} g (x)$ exists and $f (x)$ is a function that is ? to $g (x)$ for all $x$ sufficiently close to ?, but not necessarily at ? , then ?.