# What does (x+sin(x))/(x+cos(x)) equal as limit x-> "infinity"?? Thank you!!!

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Feb 11, 2018

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#### Explanation:

Divide the numerator and denominator by x, so that given function becomes

$f \left(x\right) = \frac{1 + \frac{\sin x}{x}}{1 + \frac{\cos x}{x}}$.

Now as $x \to \infty$. $\frac{\sin x}{x} \to 0$, because sin x would oscillate between +1 and -1, which in either case divided by $\infty$ would be 0. Thus the limit of the numerator would be 1. Like wise the limit of the denominator would also be 1.
Thus limit as a whole would be 1

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