Chapter 1: Q. 18 (page 135)

Suppose f and g are functions such that $lim_{x \to 3} f (x) = 5$ , $lim_{x \to 4} f (x) = 2$ , and $lim_{x \to 3} g (x) = 4$ . Given this information, calculate the limits that follow, if possible. If it is not possible with the given information, explain why.

Short Answer

Expert verified

$lim_{x \to 3} f (g (x)) = 2$

Step by step solution

Step 1. Given information.

We have to find the value of $lim_{x \to 3} f (g (x))$

Given values are:

role="math" localid="1648293838557" $lim_{x \to 3} f (x) = 5 lim_{x \to 4} f (x) = 2 lim_{x \to 3} g (x) = 4$

Step 2. Find the value

The value can be calculated as follows:

$lim_{x \to 3} f (g (x)) = f (lim_{x \to 3} g (x)) = f (4) = lim_{x \to 4} f (x) = 2$

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Suppose f and g are functions such that $lim_{x \to 3} f (x) = 5$ , $lim_{x \to 4} f (x) = 2$ , and $lim_{x \to 3} g (x) = 4$ . Given this information, calculate the limits that follow, if possible. If it is not possible with the given information, explain why.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value

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Suppose f and g are functions such that limx→3 f(x)=5, limx→4 f(x)=2, and limx→3 g(x)=4. Given this information, calculate the limits that follow, if possible. If it is not possible with the given information, explain why.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Decision Maths

Mechanics Maths

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Suppose f and g are functions such that $lim_{x \to 3} f (x) = 5$ , $lim_{x \to 4} f (x) = 2$ , and $lim_{x \to 3} g (x) = 4$ . Given this information, calculate the limits that follow, if possible. If it is not possible with the given information, explain why.