Evaluate `underset(trarr0)(Lt)(f(2+t)-f(2))/t`, where `f(x) = 4x^3`.

Evaluate: underset(-2)overset(2)int(f(x) dx where f(x) = {:{(2x-1,-2lexle1),(3x-2,1lexle2)

Evaluate underset(-1)overset2int f(x)dx , where f(x)=|x+1|+|x|+|x-1|

Find f’(2) and f’(5), where f(x) =x^2+7x+4 .

Find underset(xrarr0)f(x) where f(x)={(2x+3, xle0),(3(x+1), x>0):}

Find a if f’ (a) =0, where f(x) =x^3- 3x^2 + 3x-1 .

By using properties of definite integrals, evaluate the following: underset1overset4 int f(x)dx where f(x)={(2x+8,1lexle2),(6x, 2lexle4):}

Find lim_(x to 2)f(x) , where f(x) = 3|x| - 2

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

Find underset(xrarr0)lim f(x) , where f(x)={(|x|/x, xne0),(0, x=0):}