Recent content by Adblax

I somewhat understand the first part yes, however I really cannot see what to do for the second part, as I know it doesn't have cauchy convergence, however, intuitively, the supremum tends to 0 eventually, as given an x, they will both tend to 1 as p,q tends to infinity, and thus the supremum...

Homework Statement Fix a<b in R, and consider the two norms Norm(f)1:=Integralab( Modulus(f)) and Norm(f)Infinity:= sup{Mod(f(x)): a <= x <= b} on the vector space C[a,b]. This question shows that they are not equivalent. a. Show that there is K in R such that for all f in C[a,b]...

Ok cool, thanks for that :) sorry about the confusion

Sorry I thought my function was clearer :P the question is asking whether the derivative converges, not the main function, hence why I was putting the ' next to some g, but looking back at it it is quite unclear hehe.

How could that be applicable to the derivative of the function though, I do not remember anything saying that if the sequence is not uniformly convergence, then the derivative must not be uniformly convergent. The only thing I can think of is looking at the theorem about a sequence of...

Sorry, I omitted my work there, as did not think it was as relevant, I found the pointwise limit, say g, to be defined as; g(x) := {0 for x =/= k*Pi {1 for x = k*Pi For some k in the integers This shows the limit function is not continuous, I had thought about using the...

Homework Statement Let g_n : R -> R be given by gn (x) := cos2n (x), does gn' converge uniformly? Homework Equations The derivative is as follows; -2nsin(x)cos2n-1, which I have found converges pointwise to the 0 function. Formal definition of Uniform Convergence; For all e>0...