`lim_(t tooo)t(sqrt (t^(2)+1)-t)`

If the equation ||x-1|-6lim_(t rarr oo)((sqrt(2t^(2)-t-1)-sqrt(t^(2)-t+1))/(t(tan( pi/8))))|=2k has four distinct solutions,then the number of integral values of k is,

lim_(t rarr1)(sqrt(t)-1)/(t^((1)/(3))-1)

Q.6 lim_(t rarr oo)(e^(t^(2)-1))/(e^(t^(2)+1))

lim_(t rarr oo)(e^(t^(2))-1)/(e^(t^(2))+1)

Given that lim_(x to oo)(int_(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1 , then find the values of a and b.

lim_(t to0)(1-(1+t)^(t))/(In (1+t)-t) 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

int(dt)/(t+sqrt(a^(2)-t^(2)))