Q. 47 - Calculus

Question

Calculate each limit in Exercises 35–80.

$\underset{x\to 0}{\lim } \frac{x}{x^2-x}$

Step-by-Step Solution

Answer

The limit is - 1.

Step 1. Given Information:

Given expression: $\underset{x\to 0}{\lim } \frac{x}{x^2-x}$

We want to find the limit of given expression.

Step 2. Solution:

Take x common form denominator we get:

$$\begin{gathered} \underset{x\to 0}{\lim } \frac{x}{x^2-x} \\ =\underset{x\to 0}{\lim } \frac{x}{x(x-1)} \\ =\underset{x\to 0}{\lim } \frac{1}{x-1} \end{gathered}$$

Now put limit we get

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