Find the limit of cos(x)/(x^2) as x approaches infinity

 Exercise

$\lim_{x\to\infty}\left(\frac{\cos\left(x\right)}{x^2}\right)$

 

The limit of the product of two functions is equal to the product of the limits of each function

$\lim_{x\to\infty }\left(\frac{1}{x^2}\right)\lim_{x\to\infty }\left(\cos\left(x\right)\right)$

 

Evaluate the limit $\lim_{x\to\infty }\left(\frac{1}{x^2}\right)$ by replacing all occurrences of $x$ by $\infty $

$\frac{1}{\infty ^2}\lim_{x\to\infty }\left(\cos\left(x\right)\right)$

 

Infinity to the power of any positive number is equal to infinity, so $\infty ^2=\infty$

$\frac{1}{\infty }\lim_{x\to\infty }\left(\cos\left(x\right)\right)$

 

Any expression divided by infinity is equal to zero

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