Use L'opital to find the following limit:

Second Q (unrelated):

Use the definition of a derivative (which I know) to show that cos x is the derivative of sin x.

^ Ok for this I wrote it out with the h's as per normal. I figured, Change the numerator using sina-sinb = 2sin(x-y/2)cos(x+y/2) but then I'm a little brammed.

For the first q, the l'Opital, I make it zero but I'm having trouble convincing myself. Both the derivatives are 0 at x=0?