Q. 6 - Calculus

Question

In Exercises 3–6, $\underset{x\to c}{\lim }f\left(x\right)=L$ and $\underset{x\to c}{\lim }g\left(x\right)=M$ for some

real numbers L and M. What, if anything, can you say about$\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$ in each case?

$L=0$ and $M=0$.

Step-by-Step Solution

Answer

$\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}=0$, It is zero.

Step 1. Given Information.

The functions are $\underset{x\to c}{\lim }f\left(x\right)=L$ and $\underset{x\to c}{\lim }g\left(x\right)=M$ , Where L and M are real numbers.

$L=0, M=0$.

Step 2. Explanation.

Check $\underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$.

We have L and M both zero.

So, 

$$\begin{gathered} \underset{x\to c}{\lim }\frac{f\left(x\right)}{g\left(x\right)}=\frac{0}{0} \\ =0 \end{gathered}$$