Real Analysis : Proof using an Integral and Mean Value Theorem

For numbers a1,....,an, define p(x) = a1x +a2x^2+....+anx^n for all x. Suppose that: (a1)/2 + (a2)/3 +....+ (an)/(n+1) = 0 Prove that there is some point x in the interval (0,1) such that p(x) = 0

analysis proof 2

Note: If you have already answered this exact question please do not answer it again. I would like an answer from a different T.A. Thanks Say abs = absolute value. Suppose that the function f:[a,b]->R is Lipschitz; that is , there is a number c such that: abs(f(u) - f(v)) <= (c)abs(u-v) for all u and v in [a,b]. Let P be a partition of [a,b] and R(f,P) be a Riemann sum based on P. Prove that abs((R(f,P)) - (the integral from a to b of f)) <= ||P||(b-a)

Intervals

Please see the attached file for full problem description.

Random Generator

For the equation RAND = (ac+m)MOD MAX , if the set of random numbers is known, is it possible to calculate a,c and m?

Matlab help for solving non-linear equations

[note: suggested number of credits may be modified if necessary] Hi, Part (1/2) I need help/advice in solving non-linear equations using Matlab. My focus is on the - Bisection method - Regula falsi - Muller's method (if possible) I have seen programs for the above methods on the internet, but I could not see *examples* how to use these programs. So, if you wish to point me to a site or two, I need practical examples. Also, I need to know how to find complex roots using the Newton-Raphson method. Part (2/2) I also need help to use Matlab to solve simultaneous equations using the Gauss-Jordan elimination method (with normalization) thanks