Question

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

$\underset{x\to 4}{\lim }(5x^2-2x+3)$

Short answer

The value of limit of the given function is$75$.

Step-by-step solution

Step 1. Given information.

The limit of function is given here,

$\underset{x\to 4}{\lim }(5x^2-2x+3)$

Step 2. Formula used.

Here, in the given question we apply limits of a difference and sum.

And after it we use limit of a constant multiple

Step 3. Simplification.

Given, $\underset{x\to 4}{\lim }(5x^2-2x+3)$

$\begin{array}{c}\underset{x\to 4}{\lim }(5x^2-2x+3)\\ \underset{x\to 4}{\lim }(5x^2-2x+3)=\underset{x\to 4}{\lim }\left(5x^2\right)-\underset{x\to 4}{\lim }\left(2x\right)+\underset{x\to 4}{\lim }3\\ =5\underset{x\to 4}{\lim }{x}^2-2\underset{x\to 4}{\lim }x+\underset{x\to 4}{\lim }3\\ =5\left(4^2\right)-2\left(4\right)+3\\ =5\times 16-8+3\\ =80-8+3\\ =75.\end{array}$

therefore, our final answer is$75.$