A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back and forth along a straight line given by the equation s = 2 sin(at) + 2 cos(nt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (1) (1, 2] cm/s (1) [1, 1.1] cm/s (iII) [1, 1.01] cm/s (iv) [1, 1.001] cm/s

Find the slope of the tangent line to the sine function at the origin. y 2 y= sin(7 x) 1 Compare these values with the number of complete cycles in the interval [0, 2n]. O The slope is half the the number of cycles in the interval. O The slope is twice the number of cycles in the interval. O There is no relationship between slope and number of cycles. O The slope squared gives the number of cycles in the interval. O The slope is equal to the number of cycles in the interval.

Question #38

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The height of a buoy on a lake is changing during a storm. The height's rate of change can be modeled by r(t) = 0.5 cos(0.2t) feet per second where t is measured in seconds. Is the buoy's height increasing or decreasing at time t = 10 seconds? Why?