Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (nautical miles per hour; a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day. a. Start counting time with t = 0 at noon and express the dis- tance s between the ships as a function of t. b. How rapidly was the distance between the ships changing at noon? One hour later? c. The visibility that day was 5 nautical miles. Did the ships ever sight each other? d. Graph s and ds/dt together as functions of t for -1 SIS3, using different colors if possible. Compare the graphs and reconcile what you see with your answers in parts (b) and (c). e. The graph of ds/dt looks as if it might have a horizontal as- ymptote in the first quadrant. This in turn suggests that ds/dt approaches a limiting value as t0o. What is this value? What is its relation to the ships' individual speeds?

You will be graded on your written work as well as your answer. You and Austin start at the same place when a dinosaur attacks! At t = 0 hours, you run North at 3 miles/hour while Austin runs West at 9 miles/hour. At the bottom you will answer, "how fast is the distance between us changing at t = 0.5 hours?" In your written work: a) Draw a picture and clearly label the variables. b) What relationship should you use to help you? (some equation from geometry, using your picture and your variables.) Write the relationship using the variables from your picture. c) Use implicit differentiation to take the derivative of your relationship. You do not need to solve or simplify. d) How fast is the distance between us changing at t 0.5 hours? miles/hour

A. Which graph could represent the function ƒ(x) = 2 ·sec(x+77)-1? B. fix) C. D.

Complete the following steps for the given function, interval, and value of n. a. Sketch the graph of the function on the given interval. b. Calculate Ax and the grid points xo, X1, ..., Xn-