Q. 5 - Calculus

Question

Exercises 3–6, $\underset{x\to c}{\lim }f\left(x\right)=L$In  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?

Step-by-Step Solution

Answer

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

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 such as $L\ne 0$ and $M=0$.

Step 2. Explanation

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

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

So,

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