Explanation Given information : The R 1 and R 2 are increasing at rates of 0.01 ohm/sec. and 0.02 ohm/sec. The value of R 1 = 30 ohms and R 2 = 90 ohms. The total resistance R is given by the equation 1 R = 1 R 1 + 1 R 2 Formula Used: Power rule of derivative: If f ( x ) = k x n then f ' ( x ) = k ⋅ n x n − 1 Negative Exponent rule: 1 a m = a − m & a − m = 1 a m Chain rule: It states that derivative of composite function equals product of derivative of outside function with derivative of inside function. ( f ( g ( x ) ) ) ' = f ' ( g ( x ) ) ⋅ g ' ( x ) Calculation: Description Steps Rewrite the equation using the negative exponent rule 1 a m = a − m R − 1 = R 1 − 1 + R 2 − 1 Differentiate both sides of the equation R − 1 = R 1 − 1 + R 2 − 1 − 1 ⋅ R − 2 ⋅ d R d t = − 1 ⋅ R 1 − 2 ⋅ d R 1 d t + − 1 ⋅ R 2 − 2 ⋅ d R 2 d t Divide throughout the equation by -1 R − 2 ⋅ d R d t = R 1 − 2 ⋅ d R 1 d t + R 2 − 2 ⋅ d R 2 d t Rewrite the equation using the negative exponent rule a − m = 1 a m 1 R 2 ⋅ d R d t = 1 R 1 2 ⋅ d R 1 d

Calculus : The Classic Edition (with Make the Grade and Infotrac)

5th Edition

ISBN: 9780534435387

Author: Earl W. Swokowski

Publisher: Brooks/Cole

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Chapter 3.8, Problem 29E

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To find : the rate of change of total resistance R

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Chapter 3.8 Solutions

Calculus : The Classic Edition (with Make the Grade and Infotrac)

Ch. 3.8 - Prob. 1E Ch. 3.8 - Prob. 2E Ch. 3.8 - Prob. 3E Ch. 3.8 - Prob. 4E Ch. 3.8 - Prob. 5E Ch. 3.8 - Prob. 6E Ch. 3.8 - Prob. 7E Ch. 3.8 - Prob. 8E Ch. 3.8 - Prob. 9E Ch. 3.8 - A fire has started in a dry, open field and...

Ch. 3.8 - Prob. 11E Ch. 3.8 - Prob. 12E Ch. 3.8 - Prob. 13E Ch. 3.8 - Prob. 14E Ch. 3.8 - Prob. 15E Ch. 3.8 - Prob. 16E Ch. 3.8 - Prob. 17E Ch. 3.8 - Prob. 18E Ch. 3.8 - A person flying a kite holds the string 5 feet...Ch. 3.8 - Prob. 20E Ch. 3.8 - Prob. 21E Ch. 3.8 - Prob. 22E Ch. 3.8 - The ends of a water trough 8 feet long are...Ch. 3.8 - Work Exercise 23 if the ends of the trough have...Ch. 3.8 - Prob. 25E Ch. 3.8 - Prob. 26E Ch. 3.8 - Prob. 27E Ch. 3.8 - A softball diamond has the shape of a square with...Ch. 3.8 - Prob. 29E Ch. 3.8 - Prob. 30E Ch. 3.8 - Prob. 31E Ch. 3.8 - Prob. 32E Ch. 3.8 - Prob. 33E Ch. 3.8 - Prob. 34E Ch. 3.8 - Prob. 35E Ch. 3.8 - A North-South highway A and an East-West highway B...Ch. 3.8 - Prob. 37E Ch. 3.8 - Prob. 38E Ch. 3.8 - Prob. 39E Ch. 3.8 - Prob. 40E Ch. 3.8 - Prob. 41E Ch. 3.8 - Prob. 42E Ch. 3.8 - Prob. 43E Ch. 3.8 - Prob. 44E Ch. 3.8 - Prob. 45E Ch. 3.8 - Prob. 46E Ch. 3.8 - Prob. 47E Ch. 3.8 - Prob. 48E Ch. 3.8 - Prob. 49E Ch. 3.8 - Prob. 50E Ch. 3.8 - Prob. 51E Ch. 3.8 - Prob. 52E

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the rate of change of total resistance R

Solution Summary: The author explains that the rate of change of total resistance R is given by the equation 1R=1R1+1R2.

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Chapter 3.8 Solutions