Find the limit of $\displaystyle (x + 0.5cosx) / (x - 0.5sinx)$

Wofram Alpha gives 1 as the answer but I don't know how it got that answer. Is there some kind of trick I'm supposed to use?

limit - Wolfram|Alpha

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- Jan 8th 2011, 01:14 PMdurrrrrrrrL hopital question
Find the limit of $\displaystyle (x + 0.5cosx) / (x - 0.5sinx)$

Wofram Alpha gives 1 as the answer but I don't know how it got that answer. Is there some kind of trick I'm supposed to use?

limit - Wolfram|Alpha - Jan 8th 2011, 01:17 PMdwsmith
What is x approaching?

- Jan 8th 2011, 01:20 PMPlato
$\displaystyle \displaystyle \lim _{x \to \infty } \frac{{x + \frac{{\cos (x)}}{2}}}{{x - \frac{{\sin (x)}}{2}}} = \lim _{x \to \infty } \frac{{1 + \frac{{\cos (x)}}{{2x}}}}{{1 - \frac{{\sin (x)}}{{2x}}}} = 1$