Use series to evaluate the limit.
-$$\lim _ { x \rightarrow 0 } \frac { e ^ { - 4 x } - 1 } { x }$$
A) 4
B) -4
C) 1
D) 0

Question

Quizplus · Accepted Answer

The given limit can be evaluated using the Maclaurin series expansion for $e^{-4x}$, which is $1 - 4x + \frac{(4x)^2}{2!} - \frac{(4x)^3}{3!} + \cdots$. When substituting this into the expression and simplifying, the terms cancel out leaving $-4$ as the limit as $x$ approaches 0.

Use Series to Evaluate the Limit lim⁡x→0e−4x−1x\lim _ { x \rightarrow 0 } \frac { e ^ { - 4 x } - 1 } { x }x→0lim​xe−4x−1​

Use Series to Evaluate the Limit $\lim _ { x \rightarrow 0 } \frac { e ^ { - 4 x } - 1 } { x }$