Recent content by jj1986

Homework Statement Show that for all integers n \geq 1, cos(2x) + cos(4x) + ... + cos(2nx) = \frac{1}{2} (\frac{sin((2n+1)x)}{sin(x)}-1) Use this to verify that \sum_{n=1}^{\infty}(\int_{0}^{\pi} x(\pi-x)cos(2nx)dx) = \frac{-1}{2}\int_{0}^{\pi} x(\pi-x)dx) Homework Equations...

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My mistake I misread the problem I need to show that for any t > 1 | ( log(t) - \int^{t+1}_{t}log(x)dx ) - \frac{1}{2t} | < \frac{1}{6t^{2}}

The problem is correct as stated and makes sense. I need to show that for any t > 1 | ( log(t) - \int^{t+1}_{t}log(x)dx ) - \frac{t}{2} | < \frac{t^2}{6} Graphing it isn't really sufficient proof

Homework Statement Prove if t > 1 then log(t) - \int^{t+1}_{t}log(x) dx differs from -\frac{t}{2} by less than \frac{t^2}{6} Homework Equations Hint: Work out the integral using Taylor series for log(1+x) at the point 0 The Attempt at a Solution Using substitution I get...

anyone?

Homework Statement Let U \subset \Re^{2} be open, and f,g: U \rightarrow \Re are continuous, and \int^{b}_{a} ( \int^{d}_{c} f(x,y) dy ) dx = \int^{b}_{a} ( \int^{d}_{c} g(x,y) dy ) dx for every rectangle [a,b] x [c,d] in U. Show that f = g. Homework Equations The Attempt at a...