A graphing calculator is required for the following problem.

For 0 t 2, a particle is moving along the x-axis. The position of the particle is given by x(t) =e^(1/2)cos(t/2). The velocity of the particle is given by v(t) = 1/2 e^(t/2) (cos (t/2) sin (t/2)).

a) Find the time t at which the particle is farthest to the left. Justify your answer.

b) Is the speed of the particle increasing or decreasing at time t = ? Justify your answer.

c) The total distance traveled by the particle can be expressed as the integral from 0 to k v(t) dt v(t) dt from pi to 2pi What is thevalue of k? Justify your answer.