lim x->0 (x)sin(x)/1-cos(x).

Question

They both go to 0 so 0/0.

now take L'H
and product rule of top?
lim x->0 (1)sin(x)+ cos(x)(x)/1-cos(x)

what next? how do i solve from here?

Answer 1

derivative of top / derivative of bottom
(x cos x + sin x) / (sin x)

(x cos x/sin x) + 1

x (1 -x^2/2 ....)/(x -x^3/3 ....) + 1

x/x + 1

2

Answer 2

or, using the rule again,
(cosx - x sinx + cosx)/cosx
= (2cosx - x sinx)/cosx
= (2-0)/1
= 2