`lim_(t->1)(sqrt(t)-1)/(t^(1/3)-1)`

Compute lim_(t to 1) (sqrtt-1)/(t-1)

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

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

lim_(t rarr(1)/(2))(4t^(2)-1)/(8t^(3)-1)

For the curve x=t^(2)-1,y=t^(2)-t, the tangent line is perpendicular to x -axis,then t=(i)0(ii)prop(iii)(1)/(sqrt(3))(iv)-(1)/(sqrt(3))

lim_(x rarr1^(+))int_(x)^(4)(sqrt(t)+3)/(sqrt(t-1))dt

lim_(t rarr0)[cot^(-1)(t^2/2)]

If y = cos^(-1) ((1)/( sqrt(1+t^(2)))), x = sin^(-1) (sqrt((t^(2))/(1 + t^(2)))), "find " (dy)/(dx)

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,