w08e - Math 151, Workshop 8 1. A flagpole is 40 feet high...

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Unformatted text preview: Math 151, Workshop 8 1. A flagpole is 40 feet high and stands on level ground. A flag is attached to a 120 foot rope passing through a pulley at the top of the flagpole. The other end of the rope is tied to a car at ground level. If the car is driving directly away from the flagpole at 3 ft/sec, how fast is the flag rising when the top of the flag is 20 feet off the ground? 2. Two circles have the same center. The inner circle has radius r which is increasing at the rate of 3 inches per second. The outer circle has radius R which is increasing at the rate of 2 inches per second. Suppose that A is the area of the region between the circles. At a certain time, r is 7 inches and R is 10 inches. What is A at that time? How fast is A changing at that time? Is A increasing or decreasing at that time? 3. The numbers R1 , R2 , R3 , and R satisfy the following equation: r R 1 1 1 1 + + = . R1 R2 R3 R (The total resistance R, of a circuit composed of parallel resistances R1 , R2 , and R3 .) a) If R1 = 1 and R2 = 2 and R3 = 3, compute R exactly. b) If both R1 and R3 are held constant, and R2 is increased by .05, what is the approximate change in R? c) If both R1 and R2 are held constant, and R3 is increased by .05, what is the approximate change in R? 4. In this problem, f (x) = 1 - cos x. 1+x a) Graph f (x) in the window 0 x 6 and -1 y 1.5. b) Write an equation showing how xn , an approximation for a root of f (x) = 0, is changed to an improved approximation, xn+1 , using Newton's method. Your equation should use the specific function in this problem. c) Suppose x0 = 2. Compute the next two approximations x1 and x2 . Explain what happens to the sequence of approximations {xn } as n gets large. You should use both numerical and graphical evidence to support your assertion. d) Suppose x0 = 4. Compute the next two approximations x1 and x2 . Explain what happens to the sequence of approximations {xn } as n gets large. You should use both numerical and graphical evidence to support your assertion. ...
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This note was uploaded on 03/24/2011 for the course PHYSICS 123 taught by Professor Madey during the Spring '08 term at Rutgers.

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