Find the limit, if it exists.
-$$\lim _ { x \rightarrow 1 } \frac { x ^ { 4 } - 1 } { x - 1 }$$
A) Does not exist
B) 0
C) 4
D) 2

Question

Quizplus · Accepted Answer

We can use the fact that $a^2 + ab + b^2 = (a - b)^3$ to rewrite the limit as
\begin{align*}
\lim _ { x ightarrow 1 } \frac { x ^ { 4 } - 1 } { x - 1 } &= \lim_{x ightarrow 1} \frac{(x^2 + 1)(x^2 - 1)}{x-1} \
&= \lim_{x ightarrow 1} \frac{(x^2+1)(x-1)(x+1)}{x-1} \
&= \lim_{x ightarrow 1} (x^2+1)(x+1) \
&= 2 \cdot 2 = 4.
\end{align*}
Thus, the answer is (C).

Find the Limit, If It Exists lim⁡x→1x4−1x−1\lim _ { x \rightarrow 1 } \frac { x ^ { 4 } - 1 } { x - 1 }x→1lim​x−1x4−1​

Find the Limit, If It Exists $\lim _ { x \rightarrow 1 } \frac { x ^ { 4 } - 1 } { x - 1 }$