Recent content by celtics2004

Homework Statement Let U be an open interval in R, let f : U \rightarrow R be infinitely differentiable and let a \in U. Prove that if f has a zero arbitrarily close to a then f^{(n)}(a) = 0 for all n \geq 0. Homework Equations The Attempt at a Solution f is differentiable so f...

Thanks for your replies. I think I may have figured it out but I'm not very confident in my solution as this subject is still a little confusing. Let F(t,y) = \int^{d}_{c} ( \int^{t}_{a} f(x,y) dx ) dy. Then d/dt F(t,y) = d/dt \int^{d}_{c} ( \int^{t}_{a} f(x,y) dx ) dy. Using...

Homework Statement I am asked to compute d/dt of _{c}\int^{d} ( _{a}\int^{t} f(x,y)dx)dy for t \in (a,b) for a problem involving differentiation under the integral sign. [a,b] , [c,d] are in closed intervals in \Re f a continuous real valued function on [a,b] x [c,d] Homework...