Find the limit.
$\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x }$
A) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = - 9$
B) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = 8$
C) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = 7$
D) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = - 7$
E) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = 9$

Question

Find the limit. 
 $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x }$ 
A) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = - 9$
B) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = 8$
C) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = 7$
D) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = - 7$
E) $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = 9$

Quizplus · Accepted Answer

This limit can be solved using L'Hôpital's Rule, which states that if the limit of a function as x approaches a point is of the form 0/0 or ∞/∞, the limit of the function is the same as the limit of its derivative. Applying L'Hôpital's Rule:$\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x } = \lim _ { x \rightarrow 0 } \frac { d/dx(1 - e ^ { - 7 x }) } { d/dx(x) }$Taking the derivative of the numerator and the denominator gives:$\lim _ { x \rightarrow 0 } \frac { 0 + 7e ^ { - 7 x } } { 1 } = 7e^0 = 7$Therefore, the correct answer is 7, which corresponds to choice C.

Find the Limit lim⁡x→01−e−7xx\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x }limx→0​x1−e−7x​

Find the Limit $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { - 7 x } } { x }$