$\text { Use a graphing utility to graph the function } f ( x ) = \frac { x ^ { 2 } - 2 x + 4 } { x ^ { 3 } + 8 } \text { and determine the }$ one-sided limit $\lim _ { x \rightarrow - 2 ^ { + } } f ( x )$.
A) $- \infty$
B) $\infty$
C) 0
D) 12
E) 8

Question

Quizplus · Accepted Answer

When approaching -2 from the right, the denominator of the function $f(x) = \frac{x^2 - 2x + 4}{x^3 + 8}$ approaches 0 because $x^3 + 8$ factors into $(x + 2)(x^2 - 2x + 4)$, and the numerator remains positive. As $x$ approaches -2 from the right, the denominator approaches 0 from the positive side, causing the value of the function to approach $\infty$.