Find the limit of x^5e^((-x)/100) as x approaches infinity

 Exercise

$\lim_{x\to\infty}\left(x^5e^{-\frac{x}{100}}\right)$

 

Evaluate the limit $\lim_{x\to\infty }\left(x^5e^{\frac{-x}{100}}\right)$ by replacing all occurrences of $x$ by $\infty $

$\infty ^5\cdot e^{\frac{- \infty }{100}}$

 

Infinity to the power of any positive number is equal to infinity, so $\infty ^5=\infty$

$\infty \cdot e^{\frac{- \infty }{100}}$

 

Negative infinity divided by a positive number equals negative infinity

$\infty \cdot e^{- \infty }$

 

Apply the formula: $n^{- \infty }$$=0$, where $n=e$

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