lect116_13rev_f11

lect116_13rev_f11 - Thursday, October 6 Lecture 13 :...

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Thursday, October 6 Lecture 13 : Differentials and linearization . (Refers to Section 4.1 in your text) Students who have mastered the content of this lecture know about : The definition of the differential of a function f(x), the linearization of f(x) near x 0 . Students who have practiced the techniques presented in this lecture will be able to : Compute the differential of a function, approximate the value of a function by linearization. 13.1 Definition If y = f ( x ), we define the differential of f(x) , df or dy , as being for some number x 1 . ( Note : In dy = f ( x )( x 1 x ) = f ( x ) x the term which is the argument of f is the term which is subtracted in x .) 13.1.1 Example Suppose y = x 2 + x . Then dy = (2 x + 1) x . Observe that the value of dy depends on the value of x and the length of the x -interval. We could also write dy = d ( x 2 + x ) = (2 x + 1) x .
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.

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lect116_13rev_f11 - Thursday, October 6 Lecture 13 :...

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