hw-8 - dy dx = 1 1 + x 2 for the derivative of y = tan-1 (...

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Math 1110 Homework 8 Name: Due 10/20 or 10/21 in class GRADES Text exercises / 20 Pres probs / 20 Staple / 1 Please print out these pages. Write your answers to the “text exer- cises” on separate paper and staple it to these pages. You should include computational details. These problems will be assessed for completeness. Always write neatly and legibly. Please answer the “presentation problems” in the spaces provided. Include full explanations and write your answers in complete, mathemat- ically and grammatically correct sentences. Your answers will be assessed for style and accuracy, and you will be given written feedback on these problems. Text exercises. Please do the following problems from the book. § 3.8 #2, 5, 8, 10, 16, 23, 28, 32, 36, 44, 50, 58, 68, 74, 81, 94, 96, 98 § 3.9 #4, 8, 10, 14, 15, 20, 22, 27, 32, 40, 48, § 3.10 #2, 8, 14, 18, 23, 26, 30, 33, 37, 41 Question 1. (8 points) Derive the formula
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Unformatted text preview: dy dx = 1 1 + x 2 for the derivative of y = tan-1 ( x ) by differentiating both sides of the equivalent equation tan ( y ) = x. Math 1110 (Fall 2011) HW8 Presentation Problems 2 Question 2. (12 points) Water is slowly leaking out of a bowl at a rate of in 3 /min , as shown in the gure below. The bowl is a perfect hemisphere with radius 10 inches. If the water level is y inches, the volume of water in a hemispherical bowl of radius R is V = 3 y 2 ( 3R-y ) . Cross section R y R=10 r The bowl y (a) At what rate is the water level changing when the water is 8 inches deep? (b) What is the radius r of the waters surface when the water is y inches deep? (c) When the water level is 4 inches deep, the water level is changing at a rate of 1 64 inches per minute. At what rate is the radius of the water changing at that time?...
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hw-8 - dy dx = 1 1 + x 2 for the derivative of y = tan-1 (...

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