Limits of exponential functions Calculator

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Example

Created on 2024-06-20Asked by Madison Wright (Solvelet student)

Evaluate the limit

\lim_{x \to \infty} e^{-x}

Solution

To evaluate the limit

\lim_{x \to \infty} e^{-x}

, observe that as

x

approaches infinity,

-x

approaches negative infinity. The exponential function

e^x

grows rapidly as

x

increases. Conversely,

e^{-x}

approaches zero as

-x

decreases without bound. Therefore:

\lim_{x \to \infty} e^{-x} = 0

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Some of the related questions asked by Isabella Carter on Solvelet

1. Find the limit

\lim_{{x \to \infty}} \frac{{e^x}}{{x}}

.2. Evaluate the limit

\lim_{x \to -\infty} \frac{e^x}{x}

DefinitionExponential functions limit the behavior of functions with exponential terms as the input approaches a particular value. They are very important in calculus for modeling growth, decay, and asymptotic behavior. Example:limx→∞e−x=0 because exponential decay is so rapid that e−x approaches zero as x gets larger.

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