Approximate the limit accurate to three decimal places. $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x }$
A) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx - 54.598$
B) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx 54.598$
C) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx - 90.017$
D) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx 90.017$
E) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx 32.786$

Question

Approximate the limit accurate to three decimal places.  $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x }$ 
A) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx - 54.598$
B) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx 54.598$
C) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx - 90.017$
D) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx 90.017$
E) $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x } \approx 32.786$

Quizplus · Accepted Answer

This limit is a classic example of an exponential limit that can be solved using the definition of $e$, where $e = \lim _ { x \rightarrow 0 } ( 1 + x ) ^ { 1 / x }$. By substituting $4x$ for $x$, the limit becomes $e^4$, which is approximately $54.598$.

Approximate the Limit Accurate to Three Decimal Places lim⁡x→0(1+4x)1/x\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x }limx→0​(1+4x)1/x

Approximate the Limit Accurate to Three Decimal Places $\lim _ { x \rightarrow 0 } ( 1 + 4 x ) ^ { 1 / x }$