Chapter 12.1, Problem 46E

To determine

To find: Find the limit by direct substitution.

Answer to Problem 46E

The value of limit is $\underset{x\to -2}{\lim }\left(\frac{1}{2}{x}^3-5x\right)=10$

Explanation of Solution

Given information:The given limit is $\underset{x\to -2}{\lim }\left(\frac{1}{2}{x}^3-5x\right)$

The given limit is $\underset{x\to -2}{\lim }\left(\frac{1}{2}{x}^3-5x\right)$

To evaluate the limit we directly substitute the value $x=4$ in the function.

So we get

  $\begin{array}{c}\underset{x\to -2}{\lim }\left(\frac{1}{2}{x}^3-5x\right)=\left\{\frac{1}{2}{\left(-2\right)}^3-5\left(-2\right)\right\}\\ =\left\{\frac{-8}{2}+10\right\}\\ =\left(-4+10\right)\\ =6\end{array}$