Find the limit.
-$\lim _ { x \rightarrow 1 ^ { - } } \frac { x ^ { 2 } - 5 x + 4 } { x ^ { 3 } - x }$
A) Does not exist
B) 0
C) -$\infty$
D) $\infty$

Question

Quizplus · Accepted Answer

As $x$ approaches 1 from the left, the denominator $x^3 - x$ approaches 0, and since it factors to $x(x-1)(x+1)$, it is negative just to the left of 1. The numerator $x^2 - 5x + 4$ approaches 0 as well, but remains positive close to 1. Thus, a positive numerator over a negative denominator approaching 0 results in the limit going to $-\infty$.

Find the Limit lim⁡x→1−x2−5x+4x3−x\lim _ { x \rightarrow 1 ^ { - } } \frac { x ^ { 2 } - 5 x + 4 } { x ^ { 3 } - x }limx→1−​x3−xx2−5x+4​

Find the Limit $\lim _ { x \rightarrow 1 ^ { - } } \frac { x ^ { 2 } - 5 x + 4 } { x ^ { 3 } - x }$