Is the limit as x approaches zero of sin(x)/(2x) undefined

The limit as x->0 of (sin x)/x is 1. That's one of the two fundamental limits proved in order to discover the derivatives of the sine and cosine functions. (It's usually a "squeeze" proof, based on a geometric argument. Check your textbook in the section that discusses derivatives of trig functions.)

That's a fact that you can use in similar limit problems. Your limit is equivalent to:

lim/x->0 (1/2) (sin x)/x = (1/2) lim/x->0 (sin x)/x = (1/2)(1) = 1/2

PS: The other trig limit to memorize is lim/x->0 (1 - cos x)/x = 0.

It is defined, as follows --->

(a) As x approaches 0, sin(x) approaches x --->

(b) Then sin(x)/(2x) approaches (x)/(2x) = 1/2, in the limit.

lim sin(x)/(2x) =0/0 yes is undefined
x->0