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- Consider the parametric equation x = t2 - 1 and y = t2 + 2t. (a) find (dy)/(dx) and (d2y)/(dx2). (b) Set up, but do not evaluate, and integral representing the arc length over the interval 2 ≤ t ≤ 4.The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt= -2^(t)sin(2^t) and dy/dt=2^tcos(2^t) for time t>=0. What is the speed of the particle when t = 2.3?d/dx(y(x)) if x and y are related by the parametric equations x = t+sint, y = t^t.
- Consider the parametric equations x = t2 - 1 and y = t2 + 2t. (a) Find (dy)/(dx) and (d2y)/(dx2). (b) Set up, but do not evaluate, an integral representing the arc length over the interval 2 ≤ t ≤ 4.Find an equation y = f (x)for the parametric curve and compute dy/dx by differentiating f (x). x = cos θ, y = cos θ + sin2 θFind an equation y = f (x) for the parametric curveand compute dy/dx by differentiating f (x). c(t) = (2t + 1, 1 − 9t)