A graphing calculator is recommended.

The displacement (in centimeters) of a particlesmoving back and forth along a straight line is given by the equations=3sin(t) +2cos(t),

wheretis measured in seconds.

(a)Find the average velocity during each time period.

(i)[1, 2]

(ii)[1, 1.1]

(iii)[1, 1.01]

(iv)[1, 1.001]

(b)Estimate the instantaneous velocity of the particle whent= 1.