Question

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

$\underset{x\to 3}{\lim }(x^3+2)(x^2-5x)$

Short answer

The value of limit of the given function is$-174.$

Step-by-step solution

Step 1. Given information.

The limit of function is given here,

$\underset{x\to 3}{\lim }(x^3+2)(x^2-5x)$

Step 2. Formula used.

We can find the limit by direct substitution.

Step 3. Simplification.

Given, $\underset{x\to 3}{\lim }(x^3+2)(x^2-5x)$

$\begin{array}{c}\lim (x^3+2)(x^2-5x)=(3^3+2)(3^2-5\times 3)\\ =(27+2)(9-15)\\ =29\times (-6)\\ =-174\end{array}$

Therefore, our final answer is$-174.$