Chapter 1: Q. 4 (page 148)

In Exercises 3–6, $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} g (x) = M$ for some real numbers L and M. What, if anything, can you say about $\lim_{x \to c} \frac{f (x)}{g (x)}$ in each case?
$L = 0$ and $M \neq 0$

Short Answer

Expert verified

$\lim_{x \to c} \frac{f (x)}{g (x)} = 0$ .

Step by step solution

Step 1. Given Information

There are two functions, $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} g (x) = M$ , where L and M are real numbers, such as $L = 0$ and $M \neq 0$ .

Step 2. Explanation.

Check $\lim_{x \to c} \frac{f (x)}{g (x)}$ .

We have M is non-zero real number and L is zero.

So, $\lim_{x \to c} \frac{f (x)}{g (x)} = \frac{0}{M} = 0$ .

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In Exercises 3–6, $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} g (x) = M$ for some real numbers L and M. What, if anything, can you say about $\lim_{x \to c} \frac{f (x)}{g (x)}$ in each case?
$L = 0$ and $M \neq 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation.

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In Exercises 3–6, limx→cf(x)=Land limx→cg(x)=Mfor some real numbers L and M. What, if anything, can you say about limx→cfxgxin each case?L=0andM≠0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises 3–6, $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} g (x) = M$ for some real numbers L and M. What, if anything, can you say about $\lim_{x \to c} \frac{f (x)}{g (x)}$ in each case?
$L = 0$ and $M \neq 0$