If `g(x)=|(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c))|,` where c is a constant, then `lim_(x rarr0)(g(x))/(x)` is equal to

If int (x+1)/(sqrt(2x-1))dx = f(x)sqrt(2x-1)+C , where C is a constant of integration, then f(x) is equal to

Let f(x) = (sec x)^(cosecx) + (cot x)^(sin x) . Then the value of Lim_(x rarr 0^(+)) f(x) is equal to

If f(x) is twice differentiable and f^('')(0) = 3 , then lim_(x rarr 0) (2f(x)-3f(2x)+f(4x))/x^(2) is

If graph of a function f(x) is shown in the adjacent figure, then Lim_(x rarr 0^(-)) [(4f(x)-6[f(x)])/(tan(2f(x)-6))] is equal to

If f(x) is the integral of (2 sin x-sin 2 x)/(x^(3)), "where x" ne 0, "then find" lim_(x rarr 0) f'(x) .

If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of the form of ax^(2)+bx+c , then the value of f(1) is

Let f(x)=|x-1|dot Then (a) f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c) f(|x|)-|f(x)| (d) none of these

Consider two differentiable functions f(x),g(x) satisfying 6intf(x)g(x)dx=x^(6)+3x^(4)+3x^(2)+c and 2 int(g(x)dx)/(f(x))=x^(2)+c, " where " f(x) gt 0 AA x in R. int (g(x)-f(x))dx is equal to