If `v = 3t^2 - 2t + 1`, find the value of t for which `(dv)/(dt) = 0`

If x=3t " and " y=(2t)/3-1 , then find the value of t for which x = 3y.

Let y=x^3-8x+7a n dx=f(t)dotI(dy)/(dt)=2a n dx=3 a t t = 0, then find the value of (dx)/(dt) at t=0.

Simplify the expression 2/t-3-2t and find the values of t for which the expression is 0.

(i) If f(x) = int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t) dt, then prove that f'(x) = 0 AA x in R . (ii) Find the value of x for which function f(x) = int_(-1)^(x) t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum.

If 2t= v^(2) then (dv)/(dt) = …….

Let x=x(t) and y=y(t) be solutions of the differential equations (dx)/(dt)+ax=0 and (dy)/(dt)+by=0] , respectively, a,b in R .Given that x(0)=2,y(0)=1 and 3y(1)=2x(1) ,the value of "t" ,for which, [x(t)=y(t) ,is :

Let y=x^3-8x+7 and x=f(t) if (dy)/(dt)=2 and x=3 at t = 0, then find the value of (dx)/(dt) at t=0.

If y=tan^(-1) [(sqrt(1+t^(2))+sqrt(1-t^(2)))/(sqrt(1+t^(2))-sqrt(1-t^(2)))] , find the value of (dy)/(dt) .

If y=int_(0)^(x)(t-1)(t-2)^(2)dt , find x for which (dy)/(dx)=0 .