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

 Exercise

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

 

Simplify $2\sin\left(x\right)\cos\left(x\right)$ using the trigonometric identity: $\sin(2x)=2\sin(x)\cos(x)$

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

 

Simplify the fraction $\frac{2\sin\left(2x\right)}{2}$ by $2$

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

 

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

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

 

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

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