Question

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

Answer 1

1

Explanation:

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

`f(x)= (1 + (sin x)/x) / ( 1+ (cos x)/x)`.

Now as `x->oo`. `(sin x)/x ->0`, because sin x would oscillate between +1 and -1, which in either case divided by `oo` 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