Estimate the following limit numerically, if it exists. $$\lim _ { x \rightarrow 1 } \frac { x - 1 } { x ^ { 2 } + 5 x - 6 }$$
A) $\frac { 1 } { 7 }$
B) 0
C) $- \frac { 1 } { 5 }$
D) $\frac { 1 } { 5 }$
E) The limit does not exist.

Question

Quizplus · Accepted Answer

The denominator can be factored as $(x+6)(x-1)$, simplifying the expression to $\frac{1}{x+6}$. Substituting $x = 1$ gives $\frac{1}{7}$.

Estimate the Following Limit Numerically, If It Exists lim⁡x→1x−1x2+5x−6\lim _ { x \rightarrow 1 } \frac { x - 1 } { x ^ { 2 } + 5 x - 6 }x→1lim​x2+5x−6x−1​

Estimate the Following Limit Numerically, If It Exists $\lim _ { x \rightarrow 1 } \frac { x - 1 } { x ^ { 2 } + 5 x - 6 }$