Chapter 1: Q. 3 (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?
$L \neq 0$ and $M \neq 0$ .

Short Answer

Expert verified

$\lim_{x \to c} \frac{f (x)}{g (x)} = \frac{L}{M}$

Step by step solution

Step 1. Given Information

The functions $\lim_{x \to c} f (x) = L$ and $\lim_{x \to c} g (x) = M$ , where L and M are real numbers.

Step 2. Explanation.

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

We have L and M are non-zero real numbers.

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

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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?
$L \neq 0$ 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→cf(x)g(x)in 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

Mechanics Maths

Theoretical and Mathematical Physics

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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?
$L \neq 0$ and $M \neq 0$ .