Q. 17 Suppose f and g are functions su... [FREE SOLUTION]

Chapter 1: Q. 17 (page 135)

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

Short Answer

Expert verified

The value of $\lim_{x 鈫� 3} \frac{f (x) - 3}{g (x)} = \frac{1}{2}$

Step by step solution

Step 1. Given information

The given limit $\lim_{x 鈫� 3} \frac{f (x) - 3}{g (x)}$ and the given values are, $\lim_{x 鈫� 3} f (x) = 5, \lim_{x 鈫� 4} f (x) = 2$ and $\lim_{x 鈫� 3} g (x) = 4$

Step 2. Calculating value of the given limits

The value can be calculated as below,

$\lim_{x 鈫� 3} \frac{f (x) - 3}{g (x)} = \frac{\lim_{x 鈫� 3} f (x) - 3}{\lim_{x 鈫� 3} g (x)} [q u o t i e n t r u l e] = \frac{\lim_{x 鈫� 3} f (x) - \lim_{x 鈫� 3} 3}{\lim_{x 鈫� 3} g (x)} [s u m r u l e] = \frac{5 - 3}{4} = \frac{2}{4} = \frac{1}{2}$

Hence,the result is $\frac{1}{2}$

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Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating value of the given limits

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating value of the given limits

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.