Question

Find the following limit: lim(x,y)->(0,1) ((e^y)*sin(xy))/x
I know the answer is e^1, but I'm not sure how to get it.

Answer 1

e^y as y-->1 is e^1 or just e

sin(xy)/x as x--> 0 and y-->1 approaches sin(0)/0

you can use L'Hopital
see http://en.wikipedia.org/wiki/L'Hôpital's_rule

Answer 2

the sin(x)/x (or sinc(x) ) approaches 1 as x-->0

here is a proof
http://www.khanacademy.org/math/calculus/limits_topic/squeeze_theorem/v/proof--lim--sin-x--x

Answer 3

Awesome. Thanks for the quick response!