" 12."x^(n-1)sin x^(n)

int x^(n-1)sin x^(n)dx

Letf(x) = lim_( n to oo) (x^(n)-sin x^(n))/(x^(n)+sin x^(n)) " for" xgt 0, x ne 1,and f(1)=0 Discuss the continuity at x=1.

consider f(x)=lim_(x-oo)(x^(n)-sin x^(n))/(x^(n)+sin x^(n)) for x>0,x!=1,f(1)=0 then

cos x*cos2x*cos4x......cos(2^(n-1)x)=(sin2^(n)x)/(2^(n)sin x)AA n in N

If underset(x to 0)lim""(x^(n)sin^(n)x)/(x^(n)-sin^(n)x) is non-zero finite, then n equals :

Show that If I _(n) =int cos ^(n) x dx, then show that I_(n) =1/n cos ^(n-1) x sin x + (n-1)/(n ) I_(n-2).

Prove that nC_ (1) sin x * cos (n-1) x + nC_ (2) sin2x * cos (n-2) x + nC_ (3) sin3x * cos (n-3) x + ... + nC_ ( n) sin nx = 2 ^ (n-1) sin nn

Discus the continuity of the function f(x)=lim_(n rarr oo)((1+sin x)^(n)+In x)/(2+(1+sin x)^(n))

If I_(n)=int x^(n)cos axdx and I_(n)=int x^(n)sin axdx then show that.(1)aI_(n)=x^(n)sin ax-nI_(n-1)