Q. 53 - Calculus

Question

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits. 

$\underset{x\to 0}{\lim }\frac{1}{x}$

Step-by-Step Solution

Answer

The limit value does not exist.

Step 1. Given information.

The given function is $\underset{x\to 0}{\lim }\frac{1}{x}$.

Step 2. Graph of the function.

The graph of the function is 

We can see,

$$\begin{gathered} As x\to 0, f\left(x\right)\to -\infty \left(Left\right) \\ As x\to 0,f\left(x\right)\to \infty ( Right) \end{gathered}$$

Therefore, the limit does not exist.