Provide an appropriate response.
-Evaluate $\lim _ { x \rightarrow 1 } \frac { x ^ { 32 } - 1 } { x - 1 } =$ by first converting it to a derivative at a particular $x - v a l u e .$
A) 31
B) 33
C) 32
D) $\frac { 1 } { 32 }$

Question

Quizplus · Accepted Answer

By converting the given limit to a derivative, we have:
$$
\begin{aligned} \lim _ { x ightarrow 1 } \frac { x ^ { 32 } - 1 } { x - 1 } &=\lim _ { x ightarrow 1 } \frac { \frac { d } { d x } \left( x ^ { 32 } - 1 ight) } { \frac { d } { d x } \left( x - 1 ight) } \ &=\lim _ { x ightarrow 1 } \frac { 32 x ^ { 31 } } { 1 } \ &=32 \end{aligned}
$$
Therefore, the answer is C.

Provide an Appropriate Response lim⁡x→1x32−1x−1=\lim _ { x \rightarrow 1 } \frac { x ^ { 32 } - 1 } { x - 1 } =limx→1​x−1x32−1​=

Provide an Appropriate Response $\lim _ { x \rightarrow 1 } \frac { x ^ { 32 } - 1 } { x - 1 } =$