[" (i) "x^(2)+x],[" (v) "3t]

Differentiate w.r.t. time. (i) y=t^(2) " " (ii) x=t^(3//2)" " (iii) y=(1)/(sqrt(t)) (iv) x=4t^(3) " " (v) y=2sqrt(t) " " (vi) y=2t^(2)+t-1 (vii) y=3sqrt(t)+(2)/(sqrt(t)) (viii) y=t^(3)sin t " " (ix) x=te^(t) (x) x= sqrt(t)(1-t)

Differentiate the following w.r.t.x (1) (3x +5) (ii) x^(-2) (iii) x^(3//2) (iv) sqrtx - (1)/(sqrtx) (v) (1)/((x +2))

Integrate the following w.r.t. x. (i) 4x^(3) , (ii) x-1/x , (iii) 1/(2x+3) , (iv) cos (4x+3) (v) cos^(2) x

Integrate the following w.r.t. x. (i) 4x^(3) , (ii) x-1/x , (iii) 1/(2x+3) , (iv) cos (4x+3) (v) cos^(2) x

The following equations give the position x(t) of a particle in four situations ( in each equation, x is meters, t is in seconds, and t gt 0 ): (1) x= 3t-2 , (2) x= - 4t^(2)-2 , (3) x= 2//t^(2) , and (4) x= -2 . (a) In which situation is the velocity v of the particle constant ? (b) In which is v in the negative x direction ?

If x = e ^(2t ) cos, 3t, then (d ^(2) x)/(dt ^(2))at t = pi //2 is

Check whether the first polynomial is factor of Second polynomial by dividing: t^2-3,2t^(4)+3t^(3)-2t^(2)-9t-12 (ii) x^(2)+3x+1,3x^(4)+5x^(3)-7x^(2)+2x+2 (iii) x^(3)-3x+1,x^(5)-4x^(3)+x^(2)+3x+1

Find (dx)/(dt) (derivative) of w.r.t. t). (i) x=(t^(2)+1)^(3) (ii) x=sqrt(t)^(3)-3 (iii) x=sin2t (iv) x=cos(2t+4) (v) x=sin^(3)t (vi) x=cos^(3)t

Let g (x,y)=x^2-yx + sin (x+y), x (t) = e^(3t) , y(t) = t^2, t in R. Find (dg)/(dt) .

Find the vaoue of each of the folllowing polynomials for the indicated value of variables: (i) p(x) = 4x ^(2) - 3x + 7 at x =1 (ii) q (y) = 2y ^(3) - 4y + sqrt11 at y =1 (iii) r (t) = 4t ^(4) + 3t ^(3) -t ^(2) + 6 at t =p, t in R (iv) s (z) = z ^(3) -1 at z =1 (v) p (x) = 3x ^(2) + 5x -7 at x =1 (vii) q (z) = 5z ^(3) - 4z + sqrt2 at z =2