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128ahw6sum10

# 128ahw6sum10 - MATH 128A SUMMER 2010 HOMEWORK 6 SOLUTION...

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MATH 128A, SUMMER 2010, HOMEWORK 6 SOLUTION BENJAMIN JOHNSON Homework 6: Due Wednesday, July 14 4.1; 2b, 4b 4.2; 9 4.3; 2a, 4a, 6a, 14 section 4.1 2. Use the forward-diﬀerence and backward diﬀerence formulas to determine each missing entry in the following tables. b. x f ( x ) f 0 ( x ) 1.0 1.0000 1.2 1.2625 1.4 1.6595 solution: We can only use the forward diﬀerence formula to get f 0 (1), and we can only use the backward-diﬀerece formula to get f 0 (1 . 4). We will compute f 0 (1 . 2) using both formulas. f 0 (1 . 0) f (1 . 2) - f (1 . 0) 0 . 2 = 1 . 2625 - 1 . 0000 0 . 2 = 1 . 3125 f 0 (1 . 4) f (1 . 4) - f (1 . 2) 0 . 2 = 1 . 6595 - 1 . 2625 0 . 2 = 1 . 985 Using Forward diﬀerence for f 0 (1 . 2) we get f 0 (1 . 2) f (1 . 4) - f (1 . 2) . 2 = 1 . 985, and using backward diﬀerence we get f 0 (1 . 2) f (1 . 2) - f (1 . 0) . 2 = 1 . 3125. 4. The data in Exercise 2 were taken from the following functions Compute the actual errors in Exercise 2, and ﬁnd error bounds using the error formulas. b.

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128ahw6sum10 - MATH 128A SUMMER 2010 HOMEWORK 6 SOLUTION...

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