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

If f(x)=x/(sinx)a n dg(x)=x/(tanx),w h e r e0ltxlt=1, then in this interval

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

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

Let f(x) be a function which is differentiable any number of times and f(2x^(2)-1)=2x^(3)f(x), AA x in R . Then f^((2010))(0)= (Here f^((n))(x)=n^(th) order derivative of f at x)

If f: R^+vecR ,f(x)+3xf(1/x)=2(x+1),t h e nfin df(x)dot

If y=f(x)=((x+3))/((x-1)),t h e n x=f(y) (b) f(1)=3 y increases with xforx<1 f is a rational function of x

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c ,t h e n f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1) f(x) has two points of extrema

If f(x)=cos^2x+s e c^2x ,t h e n f(x)<1 (b) f(x)=1 (c) 2ltf(x)<1 (d) """"f(x)ge2

A function f is defined by f(x)=1/(2^(r-1)),1/(2^r)ltxlt=1 (2^(r-1)),r="1,2,3 then the value of int_0^1f(x)dx