Question

Evaluate the limit and justify each step by indicating the appropriate limit law(s).

$\underset{t\to -2}{\lim }{(t+1)}^9(t^2-1)$

Short answer

The value of limit of the given function is$-3.$

Step-by-step solution

Step 1. Given information.

The limit of function is given here,

$\underset{t\to -2}{\lim }{(t+1)}^9(t^2-1)$

Step 2. Formula used.

The given function is a polynomial, so we can find the limit by direct substitution.

Step 3. Simplification.

Given, $\underset{t\to -2}{\lim }{(t+1)}^9(t^2-1)$

$\begin{array}{c}\text{Invalid <m:msup> element}\lim (t^2-\text{Invalid <m:msup> element}1)=(-2^2-1)\\ \text{Invalid <m:msup> element}=(4-1)\\ =(-1)\times 3\\ =-3\end{array}$

Therefore, our final answer is$-3.$