Consider [itex]sin(vx)/x[/itex] as [itex]v[/itex] approaches infinity. Now, this becomes a delta function and I have seen graphs that show this function as v increases. My question is the following: I cannot quite see why the function [itex]sin(vx)/x[/itex] becomes zero if x≠0. sin(vx) is bounded and oscillates rapidly between -1 and 1 as x is changed. But the envelope of the function is still 1/x so how come it goes to zero for all x≠0? Can someone prove this result? Thank you.