Mean Value Theorem

Mean Value Theorem - 18.01 Calculus Jason Starr Fall 2005 Lecture 8 Homework Problem Set 2 all of Part I and Part II Practice Problems Course

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18.01 Calculus Jason Starr Fall 2005 Lecture 8. September 27, 2005 Homework. Problem Set 2 all of Part I and Part II. Practice Problems. Course Reader: 2A-1, 2A-4, 2A-9, 2A-11, 2A-12. 1. Linear approximations. For a differentiable function f ( x ), the linear approximation or linearization of f ( x ) at x = a is the linear function, f ( a ) + f ( a )( x a ) . In a precise sense, this is the best approximation of f ( x ) by a linear function near x = a . For x close to a , the value of f ( x ) is close to the value of the linearization. The notation for this is, f ( x ) f ( a ) + f ( a )( x a ) for x a. Example. The linearization of, f ( x ) = e 3 x sin(2 πx ) + 5 e 3 x cos(2 πx ) , near x = 0 is, f ( x ) 5 (15 2 π ) x for x 0 .
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± ± 18.01 Calculus Jason Starr Fall 2005 In particular, for x = 0 . 02, this gives the approximate answer, f (0 . 02) 5 (15 2 π )(0 . 02) 4 . 8. The actual value is approximately 4 . 71. 2. Basic approximations. Some linear approximations occur so often, they should be committed to memory. Each of the following is the linear approximation for x 0, together with the terms in the quadratic and higher approximations. 1
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This note was uploaded on 06/03/2008 for the course MATH B6A taught by Professor Moretti during the Spring '08 term at Bakersfield College.

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Mean Value Theorem - 18.01 Calculus Jason Starr Fall 2005 Lecture 8 Homework Problem Set 2 all of Part I and Part II Practice Problems Course

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