a) Prove that converges uniformly on ( ,) b) Prove that laquo 0 e xydx converges uniformly on 1, ) c) Prove that laquo 0 ye xydx exists for each y 0, ) and converges uniformly on any a, b (0, ) but that it does not converge uniformly on 0, 1 dx...

a Since cosx 2 y 2 1 for any y and 1 0 dxx it follows from the Weie ...

a) Prove that converges uniformly on (-,). b) Prove that «0 e-xydx converges uniformly on [1, ).

Question:

a) Prove that

converges uniformly on (-ˆž,ˆž).
b) Prove that ˆ«0ˆž e-xydx converges uniformly on [1, ˆž).
c) Prove that ˆ«0ˆž ye-xydx exists for each y ˆˆ [0, ˆž) and converges uniformly on any [a, b] Š‚ (0, ˆž) but that it does not converge uniformly on [0, 1].