Evaluate: lim\(_{x→-2}\) \(\frac{x^3+8}{x+2}\).

Explanation

\(\frac{x^3+8}{x+2}\).

x\(^3\) + 8 = x\(^3\) + 23

recall that

x\(^3\) + y\(^3\) = (x+y)(x\(^2\) - xy + y\(^2\))

x = x, y = 2

x\(^3\) + 8 = (x+2)(x\(^3\) - 2(x) + 22)

\(\frac{x^3+8}{x+2} = \frac{(x+2)(x^3 - 2(x) + 22)}{x+2}\) → x\(^2\) - 2x + 4

x = -2

(-2)\(^2\) - 2(2) + 4 = 4 - 4 + 4

= 4