Question

Determine the limit. lim as x-->0 (sinx)/(2x)

Answer 1

Maybe this might help: \(\sf \frac{1}{2} \lim_{x \rightarrow 0} \frac{sin(x)}{x}\)

Answer 2

well ik the answer is 1. i just dont know how

Answer 3

The function sin(x) acts like x when it get's near zero.\[\Large\bf\sf \lim_{x\to0}\frac{\sin x}{2x}\quad=\quad \frac{1}{2}\lim_{x\to0}\frac{\sin x}{x}\quad\text{~}\quad \frac{1}{2}\lim_{x\to0}\frac{x}{x}\]

Answer 4

the answer isn't 1, and you should use l'hopitals rule

Answer 5

Pull the 1/2 out like abbot suggested, then you can maybe see what's going on.
This is related to an identity that you should probably memorize if you can:\[\Large\bf\sf \lim_{x\to0}\frac{\sin x}{x}\quad=\quad 1\]

Answer 6

of course the answer cannot be 1. look at the above identity and also pull out the 1/2

Answer 7

The limit is x when you use radians.