Chapter 2: Limits and Continuity - Section 2.2 - Limit of a Function and Limit Laws - Exercises 2.2 - Page 56: 14

$-16$

We know if $f$ is a polynomial function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$. Hence since $x^3-2x^2+4x+8$ is a polynomial, we have $\lim\limits_{x \to -2}x^3-2x^2+4x+8=(-2)^3-2(-2)^2+4(-2)+8=-8-2(4)-8+8=-8-8-8+8=-16+0=-16.$