- #1
PrudensOptimus
- 646
- 0
lim x-> inf, (x + sinx)/(x + cos x)
here's what i got:
(1 + (lim x ->inf, sinx/x))/(1 + (lim x->inf, cosx/x))
note the "1"s came from x/x from the original limit.
And lim x->inf, cosx/x becomes 0.
but I don't understand how lim x->inf, sinx/x becomes 0.
sinx/x = {1 - x^2/3! + x^4/5! - ... + ...} since x approaches infinity, that series would be 1 - inf + inf - inf, eventually it is still infinity.
so, we have (1 + inf)/(1 +0) = inf, but the text says it approaches 1, so it much be something wrong i did with the sinx/x thing.
Could someone please explain?