1. For this question refer to a ball going counterclockwise around the unit circle, centered at...

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1. For this question refer to a ball going counterclockwise around the unit circle, centered at (0, 0) with radius 1. The speed is 1 (say 1 meter/sec to have units). Assume the ball starts at angle zero. Then x = cost and y = sin t. a) How long does it take for 10 revolutions? b) At time t = TT, where is the ball? c) Where is the ball (approximately) at t = 14 seconds? 5T d) Suppose that string is cut at t = When and where would the ball hit the x-axis? Draw figure for this part and add all the information on the figure. 3 2. On the first 150 miles of a 300-mile trip, your average speed is x miles per hour and on the second 150 miles, your average speed is y miles per hour. The average speed for the entire trip is 60 miles per hour. a) Write y as a function of x. b) If the average speed for the second half of the trip cannot exceed 65 miles per hour, what is the minimum possible average speed for the first half of the trip? c) Find the limit of y as x 30+. 3. Evaluate the limit if it exists? If not, determine whether the one-sided limits exist. Show algebraic steps. lim 00 2 tanesine sin 0 4. Calculate the limit. Show algebraic steps. 3 lim (9x + x - x2) X18 1. For this question refer to a ball going counterclockwise around the unit circle, centered at (0, 0) with radius 1. The speed is 1 (say 1 meter/sec to have units). Assume the ball starts at angle zero. Then x = cost and y = sin t. a) How long does it take for 10 revolutions? b) At time t = TT, where is the ball? c) Where is the ball (approximately) at t = 14 seconds? 5T d) Suppose that string is cut at t = When and where would the ball hit the x-axis? Draw figure for this part and add all the information on the figure. 3 2. On the first 150 miles of a 300-mile trip, your average speed is x miles per hour and on the second 150 miles, your average speed is y miles per hour. The average speed for the entire trip is 60 miles per hour. a) Write y as a function of x. b) If the average speed for the second half of the trip cannot exceed 65 miles per hour, what is the minimum possible average speed for the first half of the trip? c) Find the limit of y as x 30+. 3. Evaluate the limit if it exists? If not, determine whether the one-sided limits exist. Show algebraic steps. lim 00 2 tanesine sin 0 4. Calculate the limit. Show algebraic steps. 3 lim (9x + x - x2) X18