Q. 4 - 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 $M\ne 0$

Step-by-Step Solution

Answer

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

Step 1. Given Information

There are two functions, $\underset{x\to c}{\lim }f\left(x\right)=L$and $\underset{x\to c}{\lim }g\left(x\right)=M$,  where L and M are real numbers, such as $L=0$and $M\ne 0$.

Step 2. Explanation.

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

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

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