The smallest area enclosed by `y=f(x)`, when `f(x)` is s polynomial of lease degree satisfying `lim_(x->0)[(1+(f(x))/x^3)]^(1/x)=e` and the circle `x^2+y^2=2` above the x-axis is:

The polynomial of least degree such that lim_(xto0)(1+(x^(2)+f(x))/(x^(2)))^(1//x)=e^(2) is

If f(x) is a polynomial function satisfying the condition f(x) .f((1)/(x)) = f(x) + f((1)/(x)) and f(2) = 9 then

Evaluate: intf(x)/(x^3-1)dx , where f(x) is a polynomial of degree 2 in x such that f(0)=f(1)=3f(2)=-3

Let f(x) be a polynomial of degree 2 satisfying f(0)=1, f(0) =-2 and f''(0)=6 , then int_(-1)^(2) f(x) is equal to

If f(x) be a cubic polynomial and lim_(x->0)(sin^2x)/(f(x))=1/3 then f(1) can not be equal to :

Let f(x) be a polynomial satisfying lim_(xtooo) (x^(2)f(x))/(2x^(5)+3)=6" and "f(1)=3,f(3)=7" and "f(5)=11. Then The value of f(0) is

The area enclosed between the curve y^(2)(2a-x)=x^(3) and the line x=2 above the x-axis is

Let f(x) is a polynomial satisfying f(x).f(y) = f(x) +f(y) + f(xy) - 2 for all x, y and f(2) = 1025, then the value of lim_(x->2) f'(x) is

f(x) is polynomial function of degree 6, which satisfies ("lim")_(x_vec_0)(1+(f(x))/(x^3))^(1/x)=e^2 and has local maximum at x=1 and local minimum at x=0a n dx=2. then 5f(3) is equal to

Let f(x) be a polynomial of degree 5 such that x = pm 1 are its critical points. If lim_(x to 0) (2+(f(x))/(x^(3)))=4 , then which one of the following is true?