1. During a rainy spring in the city of Fort Collins, Colorado, the following depth readings were recorded in Horsetooth Reservoir. Use the data to answer the questions that follow. (a) Find the average rate of change of the water depth between t = 60 and t = 80 days. Circle your final answer, and include the appropriate units. (b) According to the data in the chart, between what days did the depth of the reservoir increase the fastest? Compute this rate of depth increase, including units. (c) Estimate the instantaneous rate of change of the water depth at t = 60 days. Include appropriate units. t (time in days) D (depth in feet) 2. The height of a golf ball after t seconds is given by s(t) = 24t - 4.9t² meters. (a) Find the average (vertical) velocity of the golf ball on the time interval 0 ≤ t ≤ 2 seconds. (b) Find the average (vertical) velocity of the golf ball on the time interval 2.5 ≤ t ≤ 4 seconds. (c) If you've done your calculations correctly, one of your above two answers should be negative. Use a complete sentence to explain what a negative answer means in the context of this problem. x²-x-12 H--3 11x + 33 3. Use algebra to calculate the limits in parts (a) and (b) exactly, giving your answers as exact whole numbers or fractions, and use the table method to approximate the limits in parts (c) and (d). (a) lim (²+2) (b) lim (a) lim f(x) = I-2 (c) lim f(x) = H-2- 0 10 40 60 80 60 68 88 91 106 (e) lim f(x) = (c) lim h→0 4. Use the graph to calculate the limits. You may assume that one square represents one unit on the graph. If a limit does not exist, write DNE in the blank. f(x) (b) f(2)= 3 (d) lim x →0+ √h + 16-4 h (d)_lim_ f(x) = x+0+ O