If `f(x)=overset(100)underset(n=1)prod(x-n)^(n(101-n)` then find `(f(101))/(f,(101))`

If f (x) = (a-x^n)^(1//n) prove that f(f(x)) = x

If f is an odd continuous function in [-1,1] and differentiable in (-1,1) then a. f'(A)=f(1)" for some "A in (-1,0) b. f'(B) =f(1)" for some "B in (0,1) c. n(f(A))^(n-1)f'(A)=(f(1))^(n)" for some " A in (-1, 0), n in N d. n(f(B))^(n-1)f'(B)=(f(1))^(n)" for some" B in (0,1), n in N

If (1+x)^n=sum_(r=0)^n a_r x^r and b_r=1+(a_r)/(a_(r-1)) and prod_(r=1)^n b_r=((101)^(100))/(100!), then n equals to: 99 (b) 100 (c) 101 (d) None of these

If f(x)= (1 + x)^n then the value of f(0) + f'(0) + (f''(0))/(2!) + .... + (f^n(0))/(n!) is

Prove that: sum_(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)

If f: R->R be defined by f(x): x^2+1,\ t h e n\ fi n d\ f^(-1)(17)a n d\ f^(-1)(-3)dot

If f(x) satisfies the relation, f(x+y)=f(x)+f(y) for all x,y in R and f(1)=5, then find sum_(n=1)^(m)f(n) . Also, prove that f(x) is odd.

Let f:N rarr R be such that f(1)=1 and f(1)+2f(2)+3f(3)+…+nf(n)=n(n+1)f(n), for n ge 2, " then " (2010f(2010)) is ……….. .

if f(x) = (x - a_1) (x - a_2) .....(x - a_n) then find the value of lim_(x to a_1) f(x)

If f(x)= \sum_{n=1}^{\infty }(sin nx)/(4^(n)) and int_(0)^(pi)f(x) dx="log" ((m)/(n)) , then the value of (m+n) is ….