when
x=0,
this is
0/0 which is undefined, but
lim(x->0)(
sin x)/x=1, as d(sin x)/dx =
cos x = 1, dx/dx = 1, and 1/1=1.
In fact, a(sin bx)/cx = ab/c as x
approaches 0. It's
provable.
As x approaches infinity, 1/x approaches 0, and so sin(x)*(1/x) approaches 0. But it's not so simple in other equations such as (e^x)/x where you have disparate limiting factors.