Question

How would I find the limit of x to infinity of (x+sinx)/(x-sinx)?

Answer 1

looks tricky @dan815

Answer 2

@UnkleRhaukus

Answer 3

I've tried l'hop, but it doesn't lead anywhere

Answer 4

I suggest that the limit could be indeterminate, reasoning as follows:
The maximum and minimum values of sin x are 1 and -1. Therefore in the limit x tends to infinity, we get infinity/infinity which is indeterminate.

Answer 5

the answer says its 1, and when I sub it into the calculator, I get 1 as well

Answer 6

hint:
If x >0, I can rewrite your functionas follows:

\[\Large \frac{{1 + \frac{{\sin x}}{x}}}{{1 - \frac{{\sin x}}{x}}}\]
furthermore, if x>0, we have:
\[\Large - \frac{1}{x} \leqslant \frac{{\sin x}}{x} \leqslant \frac{1}{x}\]
so:
\[\Large \mathop {\lim }\limits_{x \to + \infty } \frac{{\sin x}}{x} = 0\]

Answer 7

Nice :)

Answer 8

thanks! :)

Answer 9

thank you :) I get it now

Answer 10

thank you! :)

Answer 11

The wolf gives the limit as 1.
http://www.wolframalpha.com/input/?i=limit+to+infinity+of+%28x%2Bsin+x%29%2F%28x-sin+x%29

Answer 12

yea, (1+0)/1-0)=1