# L hopital question

• Jan 8th 2011, 02:14 PM
durrrrrrrr
L hopital question
Find the limit of $(x + 0.5cosx) / (x - 0.5sinx)$

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, 02:17 PM
dwsmith
What is x approaching?
• Jan 8th 2011, 02:20 PM
Plato
$\displaystyle \lim _{x \to \infty } \frac{{x + \frac{{\cos (x)}}{2}}}{{x - \frac{{\sin (x)}}{2}}} = \lim _{x \to \infty } \frac{{1 + \frac{{\cos (x)}}{{2x}}}}{{1 - \frac{{\sin (x)}}{{2x}}}} = 1$