If `f(x) = 4x^3`, evaluate `underset(trarr0)(Lt)(f(2+t)+f(2))/(t)`.

Let f(x) be a differentiable function and f'(4) = 5, then: underset(xrarr2)lim(f(4)-f(x^2))/(x-2) equals:

If a, b and c are real numbers, then the value of underset(trarr0)(lim)((1)/(t)int_(0)^(t)(1+asinbx)^(c//x)dx) equals

Let f: R rarr R be a positive increasing function with underset(xrarrinfty)lim(f(3x))/(f(x))=1, then underset(xrarrinfty)lim(f(2x))/(f(x)) =

True or False: If f(2a-x)=-f(x) , then underset0overset(2a)int f(x)dx=0 .

If 'f' is differentiable at x = a, find (underset(xrarra)lim(x^2f(a)-a^2f(x))/(x-a))

If f(x) is of the form f(x) = a + bx + cx^2 , show that underset(0)overset(1)intf(x) dx = 1/6 [f(0)+4f(1/2)+f(1)]

Let f(x)=x^4-x^3 then find f '(2)

True or False : If underset(x rarr a)Lt f(x)g(x) exists then both underset(xrarra^+)Lt f(X) and underset(xrarra^-) Lt g(x) exist separately.

A differentiable function satisfies f(x) = underset(0) overset(x) int (f(t) cos t - cos(t - x))dt . Which of the following hold(s) good? a. f(x) has a minimem value 1-e b. f(x) has a maximum value 1-e^(-1) c. f''((pi)/(2))=e d. f'(0)=1