Homework Statement
It is a 4 parter, but i got 3 and 4 done.
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 ...
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|
Homework Statement
a) Given the definition of the divergence of a sequence {a_n} :
"For any H >0 we can find a number NH such that a_n >H, for all n>N_H"
prove that {a_n * b} diverges if {a_n } diverges for any b ≠ 0 .
b) Find the supremum and infimum for the se… 1 - 1/n } and, if...
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 *...