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Exercise

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

Step-by-step Solution

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

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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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