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Exercise

$\lim_{x\to\infty}\left(\frac{x^{\:3}}{e^x}\right)$

Step-by-step Solution

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Because polynomial functions ($x^3$) grow asymptotically slower than exponential functions ($e^x$), we can say that the expression $\lim_{x\to\infty }\left(\frac{x^3}{e^x}\right)$ tends to zero as $x$ goes to infinity

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Final answer to the exercise

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  • Solve using L'Hôpital's rule
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  • Solve using limit properties
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  • Integrate by partial fractions
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$\lim_{x\to\infty}\left(x^2e^{-x}\right)$

Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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