If `f(alpha)=f(beta)` and `n in N`, then the value of `int_alpha^beta (g(f(x)))^n g\'(f(x))*f\'(x)dx=`
(A) `1` (B) `0` (C) `(beta^(n+1)-alpha^(n+1))/(n+1)` (D) none of these

If f(x) = (a-x^n)^(1/n), a > 0 and n in N , then prove that f(f(x)) = x for all x.

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If alpha,beta(beta>alpha), are the roots of g(x)=a x^2+b x+c=0 and f(x) is an even function, then int_alpha^betae^(f((g(x))/(x-alpha)))/(e^(f((g(x))/(x-alpha)))+e^(f((g(x))/(x-beta))))= (a) |b/(2a)| (b) (sqrt(b^2-4a c))/(|2a|) (c) |b/a| (d) none of these

Let f(theta)=cottheta/(1+cottheta) and alpha+beta=(5pi)/4 then the value f(alpha)f (beta) is

The value of the integral int_alpha^beta (1)/(sqrt((x-alpha)(beta-x)))dx " for "beta gt alpha , is

If f(x)=x^(n),"n" epsilon N , then the value of f(1)-(f^(')(1))/(1!)+(f^(")(1))/(2!)-(f^''')(1)/(3!)+…+(-1)^(n)(f^(n)(1))/(n!) is

If f(x) = alphax^(n) prove that alpha = (f'(1))/n

Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1) =5 alpha'(2) =7 then find the vlaue of beta'(1)-10

If alpha,beta are zeroes of polynomial f(x) =x^(2)-p(x+1)-c , then find the value of (alpha+1)(beta+1) .

If f(x)=(cotx)/(1+cotx)andalpha+beta=(5pi)/(4) , then find f(alpha).f(beta) .