Q. 29 - Calculus

Question

Calculate each of the limits in Exercises $29-70$.

$\underset{x\to 0}{\lim } \left(x^2-1\right)$.

Step-by-Step Solution

Answer

The value of $\underset{x\to 0}{\lim } \left(x^2-1\right)$ is, $-1$.

Step 1 . Given information

$\underset{x\to 0}{\lim } \left(x^2-1\right)$.

Step 2 . The limit is calculated as below:

$\underset{x\to 0}{\lim } \left(x^2-1\right)=\underset{x\to 0}{\lim }\left(x^2\right)-\underset{x\to 0}{\lim }\left(1\right)$ [Sum rule]

                    $$\begin{gathered} ={\left(0\right)}^2-1 \\ =0-1 \\ =-1 \end{gathered}$$