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
lim x->0 (x)sin(x)/1-cos(x).
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?
2 answers
or, using the rule again,
(cosx - x sinx + cosx)/cosx
= (2cosx - x sinx)/cosx
= (2-0)/1
= 2
(cosx - x sinx + cosx)/cosx
= (2cosx - x sinx)/cosx
= (2-0)/1
= 2