(x^(2)-2x+2^(|a|))/(n^(2)-a^(2))>0

If the roots of a quadratic equation x^(2)+2px+mn=0 are real and equal, show that the roots of the quadratic equation x^(2)-2(m+n)x+(m^(2)+n^(2)+2p^(2))=0 are also equal.

f(x)=lim_(n rarr oo)((n^(n)(x+n)(x+(n)/(2))...(x+(n)/(n)))/(n!(x^(2)+n^(2))(x^(2)+(n^(2))/(4))......(x^(2)+(n^(2))/(n^(2))))) foe all x>0. Then

int([x+sqrt(a^(2)+x^(2))]^(n))/sqrt(a^(2)+x^(2))dx(n ne0)=

Prove that, int_(0)^(2pi)(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx=pi^(2) .

Prove that: int_(0)^(2 pi)(x sin^(2n)x)/(sin^(2n)+cos^(2n)x)dx=pi^(2)

The value of lim_(x rarr0)((e^(1))/(x))-(1+nx+(n^(2))/(2)x^(2))/(x^(3))(n>0) is

Evaluate int_(0)^(2pi)(xcos^(2n)x)/(cos^(2n)x+sin^(2n)x)dx

Evaluate int_(0)^(2pi)(xcos^(2n)x)/(cos^(2n)x+sin^(2n)x)dx