How is it possible that lim(x to infinity) sin(x/2)/x = 1/2? I thought it was zero.....? After all, the maximum value of the numerator is 1 in absolute value while the denominator approaches infinity, thus making the expression approaching zero.
So what's up guys? What am I missing?
If the limit is being taken as x goes to infinity, then you are correct.
I suspect that there is a typo in the book, and that the limit was supposed to have been "as x tends toward zero". If so, then the book's answer would have been correct.
Ask your instructor for correction or clarification.