Determine whether or not the following limit exists. If, so compute the limit. $\lim _ { x \rightarrow - 1 }$ $\frac { x ^ { 2 } - 1 } { x + 1 }$
A) -2
B) 1
C) does not exist
D) 0
E) none of these

Question

Quizplus · Accepted Answer

The given limit can be simplified by factoring the numerator as $(x+1)(x-1)$ and then canceling out the $(x+1)$ term in the numerator with the $(x+1)$ in the denominator, resulting in $\lim _ { x \rightarrow - 1 }$ $\frac { x ^ { 2 } - 1 } { x + 1 } = \lim _ { x \rightarrow - 1 } (x - 1)$. Substituting $x = -1$ into the simplified expression gives $(-1) - 1 = -2$.

Determine Whether or Not the Following Limit Exists lim⁡x→−1\lim _ { x \rightarrow - 1 }limx→−1​

Determine Whether or Not the Following Limit Exists $\lim _ { x \rightarrow - 1 }$