GHW7 - (b What is the percentage error Section 4.1 Maximum...

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Math 2413 Graded Homework # 7 GHW7 17 October 2011 Due Monday 10/24 in Lecture Work to be done in Blue book per syllabus Section 3.10: Linear Approximations and Differentials 1. (6 pts) Find the linear approximation of the function f ( x ) = 3 1 + x at a = 0 and use it to approximate 3 0 . 95 and 3 1 . 01. 2. (4 pts) Find the differential dy for y = cos πx and evaluate it x = 1 3 and dx = - 0 . 02 and round your results to 3 decimal places. 3. (6 pts) One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 o , with a possible error of ± 1 o . (a) Use differentials to estimate the error in computing the length of the hypotenuse.
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Unformatted text preview: (b) What is the percentage error? Section 4.1: Maximum and Minimum Values 4. (12 pts) Find the absolute maximum and absolute minimum values of the following functions at the given intervals: ( a ) f ( x ) = x 3-6 x 2 + 5 , [-3 , 5] ( b ) g ( x ) = x-2 tan-1 x, [0 , 4] Section 4.2: The Mean Value Theorem 5. (12 pts) Verify the functions satisfy the hypotheses of the Mean Value Theorem on the given inter-val. Then find all numbers c that satisfy the condition of the Mean Value Theorem ( a ) f ( x ) = x 3-3 x + 2 , [-2 , 2] ( b ) f ( x ) = ln x, [1 , 4]...
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