Let p(x) = ax^2 + bx + c be such that p(x) takes real values
for real values of x and non−real values for non−real
values of x . Prove that a = 0 and find all
possible values of c.
let U_n =∫_0 ^(+∞) ((cos(ch(nx)))/((3+x^2 )^2 ))dx
1) calculate U_n interms of n
2) find lim_(n→+∞) n U_n and lim_(n→+∞) n^2 U_n
3)study the serie Σ U_n
f(t) =∫_0 ^(+∞) (e^(−xt) /((x+t)^2 ))dx with t≥0
1) study the set of definition for f(t)
2)study the continuity of f
3)study the derivability of f
4) developp f at integr serie