Recent content by rayred

Thank you for your reply! Well for part a, I did something similar in my notes ( I think ). Unless I took notes wrong, the professor took the min and max of the interval ( so 0 and 3 respectively ), solved f at those points, then took f prime, set it equal to zero, then solved for x? Is this...

I think I have done part A properly. When you are taking f of a set, you are simply mapping each value in the set to another set right? for a, I got the set {1, 1/3, 5/3, 7} is this correct? For part B I am confused because, well to be honest I am terrible at proofs ( you can imagine how...

Homework Statement a) Find f ([0,3]) for the following function: f(x)=1/3 x^3 − x + 1 b) Consider the following function : f(x) = e^(−ax) (e raised to the power of '-a' times 'x') a, x ∈ [0,∞) Find values of a for which f is a contraction . c) Prove that for all x,y ≤ 0 | 2^x −2^y | ≤ |x−y|

@sid Thank you a bunch!

Homework Statement a) Show that the series ∑ from n = 1 to infinity 1/n^p where p converges when p > 1 and diverges for p=1. b) Prove that the following series diverges: ∑ from n = 1 to infinity sqrt(n)/n+1 c) Use an appropriate test to show whether ∑ from n = 1 to infinity [(−1)^n *...