Okay, I have a question that I am not good enough at multivariable calculus yet to answer myself. Basically, say I have the following inequality: a < sin(xy)/y < b with a < b. How can I find out what the maximum value of y is on the interval 0 < y < 1 such that the above inequality holds for some x > 0? That is, what is the biggest value of y between 0 and 1, such that for some x > 0, sin(xy)/y is between two limits a and b with a < b? Is this even possible...? Any information, hints, outright answers, scathing insults etc. would be appreciated! Thank you.