Let `f(x)=int_1^x dt/(t^3(1+t^3)^(1/3))` and `lim_(xrarroo)f(x)=(a^2-1)/a^3`, then `a^30`=

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

Let f(x)=int_(2)^(x)f(t^(2)-3t+4)dt . Then

lim_(xrarroo) ((x+2)/(x+1))^(x+3) is equal to

Let f(x)=int_(0)^(x)(dt)/(sqrt(1+t^(3))) and g(x) be the inverse of f(x) . Then the value of 4 (g''(x))/(g(x)^(2)) is________.

Let f(x) = int_(-2)^(x)|t + 1|dt , then

Let f(x)=int_(0)^(x)(e^(t))/(t)dt(xgt0), then e^(-a)[f(x+1)-f(1+a)]=

Let f(x)=1/x^2 int_4^x (4t^2-2f'(t))dt then find 9f'(4)

The value of lim_(xrarroo) ((x+3)/(x-1))^(x+1) is

Let g (x ) = x ^(C )e ^(Cx) and f (x) = int _(0)^(x) te ^(2t) (1+3t ^(2))^(1//2) dt. If L = lim _(x to oo) (f'(x ))/(g '(x)) is non-zero finite number then : The value of L . Is :

If f(x)=int_(1)^(x) (log t)/(1+t) dt"then" f(x)+f((1)/(x)) is equal to