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GHW6 - 4(6 At time t ≥ 0 the velocity of a particle...

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Math 2413 Graded Homework # 6 GHW6 10 October 2011 Due Monday 10/17 in Lecture Work to be done in Blue book per syllabus Section 3.6: Derivatives of Logarithmic Functions 1. (6 pts) Find the second derivative of the function f ( x ) = 1 9 x 3 (3 ln x - 1) + 5 and simplify your result. 2. (8 pts) Using logarithmic differentiation find (a) y 0 if y = ( e 6 x + 2 x ) 1 x (b) df du is f ( u ) = (sin ( e u )) ln u Section 3.7: Rates of Change in the Natural and Social Sciences 3. (5 pts) A weather balloon is released and rises vertically such that its distance s ( t ) above the ground during the first 10 seconds of the flight is given by s ( t ) = 7 + 2 t + t 2 , where s ( t ) is in feet and t is in seconds. (a) Find the velocity of the balloon at t = 1 , t = 4. (b) Find the velocity and acceleration (in proper units) at the instant the balloon is 51 feet above the ground.
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Unformatted text preview: 4. (6) At time t ≥ 0, the velocity of a particle moving along a straight line is v ( t ) = t 2-4 t + 3. (a) Find the particle’s acceleration each time the velocity is zero. (b) When is the particle moving forward? (c) When is the particle’s velocity decreasing? Section 3.9: Related Rates 5. (7 pts) If a snowball melts so that its surface area decreases at a rate of 1 cm 2 /min, find the rate at which the diameter decreases when the diameter is 10 cm. 6. (8 pts) Water runs into a conical tank at the rate of 9 ft 3 /min. The tank stands point down and has a height of 10 ft and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft deep?...
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