`lim_(t to0)(1-(1+t)^(t))/(In (1+t)-t)` is equal to

If int_(0)^(1)(e^(t))/(1+t)dt=a then int_(0)^(1)(e^(t))/((1+t)^(2))dt is equal to

Suppose that a and b(b!=a) are real positive numbers, the value of lim_(t to0)((b^(t+1)-a^(t+1))/(b-a))^(1//t) has the is equal to

If k=int_(0)^(1) (e^(t))/(1+t)dt , then int_(0)^(1) e^(t)log_(e )(1+t)dt is equal to

The value of lim_(n rarr oo)sum_(r=1)^(n)(sum_(t=0)^(r-1)(1)/(5^(n))*C(n,r)C(r,t)3^(t)) is equal to

lim_(x rarr0)(int_(0)^(x)(t^(2)+e^(t^(2)))^((1)/(1-cos t)))/(e^(x)-1) is equal to

If lambda=int_(0)^(1)(e^(t))/(1+t), then int_(0)^(1)e^(t)log_(e)(1+t)dt is equal to

lim_(x to 0)(int_(0)^(x^(2))(tan^(-1)t)dt)/(int_(0)^(x^(2))sin sqrt(t)dt) is equal to :

lim_(t rarr0)((1)/(t sqrt(1+t))-(1)/(t))