If `f(x)=x^n ,f(1)+(f^1(1))/1+(f^2(1))/(2!)+(f^n(1))/(n !),w h e r ef^r(x)` denotes the rth order derivative of `f(x)` with respect to `x ,` is a. `n` b. `2^n` c. `2^(n-1)` d. none of these

If f(x)=x^n w h e r en in R , then differentiation of x^n with respect to xsin x^(n-1)dot

if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) + ---+((-1)^n f''^--n times (1))/(n!)

Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th) derivative of f (x) w.r.t. x, k in N. If f^(2m) (0) != 0, m belongs to N, then m =

If f(x)=prod_(n=1)^(100)(x-n)^(n(101-n)) ; then (f(101))/(f'(101))=

Let f(x)=|{:(,1//x,logx,x^(n)),(,1,-1//n,(-1)^(n)),(,1,a,a^(2)):}| where ("where"f^(n)(x) "donotes "n^(th) derivative of f(x). (A) f^(n)(1)"is indepent of a" (B) f^(n)(1)"is indepent of n" (C) f^(n)(1)"is indepent a or n" (D) y=a(x-f^(n)(1)) represent a straight line through the origin

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

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 f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b) -1 (c) 0 (d) none of these

f(1)=1, n ge 1 f(n+1)=2f(n)+1 then f(n)=

If f(x)=(x^(4)+x^(2)+1)/(x^(2)-x+1) , the value of f(omega^(n)) (where 'omega' is the non-real root of the equation z^(3)=1 and 'n' is a multiple of 3), is ……….. .