Written Assignment 1. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If the distance s between the airplane and the radar station is decreasing at a rate of 400 km per hour when S=10 km., what is the horizontal speed of the plane? Make sure your answer includes units. 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the deck, positioned 6 meters higher than the boat. If the rope is being pulled in at a rate of 3 meters/sec, how fast is the boat approaching the dock when it is 8 meters from the dock? Make sure your answer includes units. 3. A girl is flying a kite on a string. The kite is 120 ft. above the ground and the wind is blowing the kite horizontally away from her at 6 ft/sec. At what rate must she let out the string when 130 ft of string has been released? Make sure your answer includes units. 4. Find the Linearization of J () = sin at a = 2. Provide your answer as () =? 5. Use Linear Approximation to estimate e .. Provide your answer in 2 decimal places. Do not use a calculator. Show work for credit. 6. Calculate the locations of maximums and minimums of the following functions: Show work in details. . f(x) = 23 - 3x + 2 . f(x) = x - 8x2 +3 /. Find the exact x-value where the function J (x) = x + In (x2 - 1) attains a maximum value. An estimated answer or a calculator answer will not earn any credit. B. Using the Mean Value Theorem and Rolle's Theorem, show that + x -1 =0 has exactly one real root. 9. If f (1) = 10 and f'(x) 2 2 for 1