My a.p. calculus teacher doesn't know how to do this problem (like many others) so he's giving us 5 points extra credit on our test if we can figure it out, but I don't know how to do it:

Question

It's as the lim-->infinity
(x+sinx)/(x+cosx)

We know the answer is 1 because it's in the back of the book but do not know how to get that answer. Yeah he ticks me off with not knowing his own material but can anyone help me?

Answer 1

Sin(x) and cos(x) are periodic functions, and the value of these function have the range of 0 to 1. The result of x+(these function) will mainly be the value of x itself.

As x approaches infinity, the effect of sin(x) and cos(x) will become smaller and smaller.

Therefore, the limit of (x+sinx)/(x+cosx) will approach one.