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Unformatted text preview: x ). Suppose we want to compute the derivative 1 at x = 0 using ﬁnite diﬀerences. Let D 1 ( h ) = f ( x + h )f ( x ) h and D 2 ( h ) = f ( x + h )f ( xh ) 2 h . Let D 3 ( h ) denote the method from Problem 8 of Section 2.2 in the textbook. Compute all of these for h = 10j , for j ∈ { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . Let e k ( h ) denote the error in D k ( h ) for k ∈ { 1 , 2 , 3 } . Plot log 10 ( e k ( h )) versus log 10 ( h ) for k ∈ { 1 , 2 , 3 } . What does the slope tell you? Can you say anything about the minimums of the curves? All the above problems (if graded) are worth 5 points each, except the ﬁnal two problems which are worth 10 points each. Study Problems (Will not be graded.) • Epperson, Section 2.1 problems: 1b, 4 (for 1b), 9 (for 1b). • Epperson, Section 2.2 problems: 2a, 2b, 3a, 3b, 9 (for 3a and 3b), 12, 14a. • Epperson, Section 2.3 problems: 1. 2...
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 Spring '08
 Rottman
 UCI race classifications, Worth1000, Natural logarithm, Logarithm, G protein coupled receptors, • Epperson

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