Subtract :
`3t ^(4) - 4t ^(3) + 2t ^(2) - 6t + 6 ` from `- 4t ^(4) + 8t ^(3) - 4t ^(2) - 2t + 11`

If u = 3t^(4) - 5t^(3) + 2t^(2) - 18t+4 , find (du)/(dt) at t = 1 .

(3t-2) / (4) - (2t + 3) / (3) = (2) / (3) -t

If f(t)=4t^(2)-3t+6 , find (i) f (0) , (ii) f (4) , (iii) f(-5) .

Let the function y = f(x) be given by x= t^(5) -5t^(3) -20t +7 and y= 4t^(3) -3t^(2) -18t + 3 where t in ( -2,2) then f'(x) at t = 1 is

Simplify each of the following 4st (s -t) - 6s^(2)(t - t^(2)) - 3t^(2) (2s^(2) - s) + 2st(s - t)

If S=(t^(3))/(3)-2t^(2)+3t+4 , then

(3t-2)/4 - (2t+3)/3 = 2/3 -t

Statement :1 If a parabola y ^(2) = 4ax intersects a circle in three co-normal points then the circle also passes through the vertr of the parabola. Because Statement : 2 If the parabola intersects circle in four points t _(1), t_(2), t_(3) and t_(4) then t _(1) + t_(2) + t_(3) +t_(4) =0 and for co-normal points t _(1), t_(2) , t_(3) we have t_(1)+t_(2) +t_(3)=0.

If a circle and the rectangular hyperbola xy = c^(2) meet in four points 't'_(1) , 't'_(2) , 't'_(3) " and " 't'_(4) then prove that t_(1) t_(2) t_(3) t_(4) = 1 .

At time t, positions of three particles A,B, and C are as follows. x_(A) = 2t + 7, x_(8) = 3t^(2) + 2t + 6, x_(C) = 5t^(3) + 4t Which of them has uniform (constant) acceleration ?