Find the limit.
-$$\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 3 } - 9 x }$$
A) 15
B) $\infty$
C) Does not exist
D) $*$

Question

Quizplus · Accepted Answer

The numerator factors as $(x-3)(x-5)$ and the denominator factors as $x(x^2-9)$. Therefore, $\frac{x^2-8x+15}{x^3-9x}=\frac{(x-3)(x-5)}{x\cdot x\cdot (x-3)}$. As $x$ approaches $0$, the function approaches $\frac{-5}{0}$ from the left and $\frac{-3}{0}$ from the right, so the limit does not exist.

Find the Limit lim⁡x→0x2−8x+15x3−9x\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 3 } - 9 x }x→0lim​x3−9xx2−8x+15​

Find the Limit $\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 3 } - 9 x }$