[tex] \lim_{x \to \ 0} \frac{(x2+2x)sin x}{(x+2)(1-cos2x)}=[/tex]

=lim x-> 0 ((x^2+2x)sin x)/((x+2)(1-cos 2x)
=lim x-> 0 (x(x+2)sin x)/((x+2)(1-cos 2x)
sederhanakan (coret) (x+2)
=lim x->0 (x sin x)/(1-(1-2sin^2 x))
=lim x->0 (x sin x)/(2sin^2 x)
=1/2