Evaluate the limit as a number, ∞, or -∞, limn →∞ e^-n

Name: Problem 17, Chapter 9: Calculus with Concepts in Calculus
Uploaded: 2022-04-13T06:40:47-08:00
Duration: 2 min 31 s
Channel: Anurag Kumar
Description: Evaluate the limit as a number, ∞, or -∞, limn →∞ e^-n

step 1 In this problem of sequence and series, we have to evaluate the limit as a number or we can eval

Question

Evaluate the limit as a number, $\infty$, or $-\infty$, $$ \lim _{n \rightarrow \infty} e^{-n} $$

   Evaluate the limit as a number, $\infty$, or $-\infty$,
$$
\lim _{n \rightarrow \infty} e^{-n}
$$

Calculus with Concepts in Calculus

Denny Gulick, Robert… 6th Edition

Chapter 9, Problem 17

Instant Answer

Solved by Expert Anurag Kumar

04/13/2022

Step 1

The expression $e^{-n}$ can be rewritten as $\frac{1}{e^n}$, so the limit becomes $$ \lim _{n \rightarrow \infty} \frac{1}{e^n} $$ Show more…

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Evaluate the limit as a number, $\infty$, or $-\infty$, $$ \lim _{n \rightarrow \infty} e^{-n} $$

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Key Concepts

Limit of a Sequence

This concept refers to the value that the terms of a sequence approach as the index goes to infinity. Evaluating limits involves determining the behavior of a sequence as it progresses indefinitely, which can result in convergence to a specific number or divergence to infinity.

Exponential Function Behavior

Exponential functions, such as e^x, exhibit specific growth or decay properties depending on the sign of the exponent. When the exponent is negative, as in e^(-n), the function represents an exponential decay, meaning it decreases rapidly towards zero as n increases.

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