i have a suggestion...pls request members
of the forum to post four to five question
so that we get time to solve them...there is
flood of questions...so little time to see all post
pls give comment if you agree wkth it...
let f(t)=Σ_(n≥1) (−1)^n ln{1+ (t^2 /(n(1+t^2 )))}
1) study the simple and uniform convergence
of Σ f_n
2)study the continuity of f
3) prove that lim_(t→+∞) f(t)=ln((2/π)) .
let f(x)= Σ_(n=1) ^∞ (((−1)^(n−1) )/(ln(nx)))
1) give D_f and study f on]1,+∞[
2)study the continjity of f and calculate
lim _(x→1) f(x) and lim_(x→+∞) f(x).
3) prove that f is C^1 on ]1,+∞[ .
let f(x)=Σ_(n=1) ^∞ (1/n) cos^n (x)sin(nx)
1)prove the convergence of this serie
2)prove that f is C^2 on R −{kπ,k∈Z}and
calculate f^′ (x)
3) give a exprrssion of f.