Find $\lim _ { x \rightarrow \infty } \frac { e ^ { 2 x } } { 1 + e ^ { 5 x } }$
A) DNE
B) 0
C) $\infty$
D) 2/5

Name: Find $\lim _ { x \rightarrow \infty } \frac { e ^ { 2 x } } { 1 + e ^ { 5 x } }$ A) DNE B) 0 C) $\infty$ D) 2/5
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Question

Quizplus · Accepted Answer

As $x$ approaches infinity, $e^{5x}$ grows much faster than $e^{2x}$, making the denominator dominate and the fraction approach 0.

Find lim⁡x→∞e2x1+e5x\lim _ { x \rightarrow \infty } \frac { e ^ { 2 x } } { 1 + e ^ { 5 x } }limx→∞​1+e5xe2x​

Find $\lim _ { x \rightarrow \infty } \frac { e ^ { 2 x } } { 1 + e ^ { 5 x } }$