Provide an appropriate response.
-Evaluate $\lim _ { x \rightarrow 1 } \frac { x ^ { 33 } - 1 } { x - 1 } =$ by first converting it to a derivative at a particular $x$-value.
A) 32
B) 33
C) $\frac { 1 } { 33 }$
D) 34

Question

Quizplus · Accepted Answer

The given limit has the form of a derivative. We can take the derivative of the function $f(x)=x^{33}$ and evaluate it at $x=1$ to get the same limit. Using the power rule of differentiation, we have $f'(x)=33x^{32}$. Therefore, $f'(1)=33$. So, the limit is equal to $33$, which corresponds to choice B.

Provide an Appropriate Response lim⁡x→1x33−1x−1=\lim _ { x \rightarrow 1 } \frac { x ^ { 33 } - 1 } { x - 1 } =limx→1​x−1x33−1​=

Provide an Appropriate Response $\lim _ { x \rightarrow 1 } \frac { x ^ { 33 } - 1 } { x - 1 } =$