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Find the limit of $\frac{e^x}{x^2}$ as $x$ approaches $\infty $

Step-by-step Solution

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Final Answer

indeterminate

Step-by-step Solution

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We could not solve this problem by using the method: Limits by Factoring

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Evaluate the limit $\lim_{x\to\infty }\left(\frac{e^x}{x^2}\right)$ by replacing all occurrences of $x$ by $\infty $

$\frac{e^{\infty }}{\infty ^2}$

Learn how to solve limits to infinity problems step by step online.

$\frac{e^{\infty }}{\infty ^2}$

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Learn how to solve limits to infinity problems step by step online. Find the limit of (e^x)/(x^2) as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(\frac{e^x}{x^2}\right) by replacing all occurrences of x by \infty . Infinity to the power of any positive number is equal to infinity, so \infty ^2=\infty. Apply a property of infinity: k^{\infty}=\infty if k>1. In this case k has the value e. Infinity divided by infinity (\frac{\infty}{\infty}) is an indeterminate form.

Final Answer

indeterminate

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Function Plot

Plotting: $\frac{e^x}{x^2}$

Main Topic: Limits to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.

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