Chapter 4 - Differentiation

Chapter 4 - Differentiation - Chapter 4 Differentiation...

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Chapter 4 – Differentiation Section 4.1 – The Algebra of Derivatives Pg 69, Definition – Let I be an open interval containing the point x o . Then the function is said to be differentiable at x o if exists, in which case we denote this limit by and call it the derivative of at x o ; that is If the function is differentiable at every point in I, we say that is differentiable and call the function the derivative of . Pg 71, Proposition 4.1 – For a natural number n, define for all x in R. Then the function is differentiable and Pg 72, Proposition 4.2 – Let I be an open interval containing the point x o , and suppose that the function is differentiable at x o . Then is continuous at x o . Pg 72, Theorem 4.3 – Let I be an open interval containing the point x o , and suppose that the functions and and differentiable at x o . Then (i) is differentiable at x o and (ii) is differentiable at x o and (iii)if for all x in I, then is differentiable at x o and Pg 74, Proposition 4.4 – For an integer n, define
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This note was uploaded on 11/10/2011 for the course MATH 511 taught by Professor Higdon during the Spring '11 term at Oregon State.

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Chapter 4 - Differentiation - Chapter 4 Differentiation...

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