chapter3(7) - MATH1010 Chapter 3 cont and Chapter 4 1...

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MATH1010: Chapter 3 cont… and Chapter 4 1 DIFFERENTIATION RULES cont… Linear Approximations and Differentials (3.11, pg. 262) cont… Recall: Last day, we introduced the equation for finding a linear approximation. Example: Find a linearization of x x f 1 ) ( = at 2 = a . Notes: what we’re doing is making sure that the values of ) ( x f and ) ( x L at the point a x = match, as do the values of the slopes there ) ( x L is a function of x . The approximation is better the closer x is to a .
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MATH1010: Chapter 3 cont… and Chapter 4 2 Higher order approximations are possible. Question: How does the behaviour of the approximation compare to that of the original function? Recall: dx dy x f = ) ( We call dx and dy differentials , and they are related through dx x f dy ) ( = Geometrically: One can think of dy as the amount that the tangent line rises or falls when x changes by dx , while y Δ is the amount that the curve rises or falls when x changes by dx.
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This note was uploaded on 09/13/2008 for the course MATH 1010u taught by Professor Kim during the Spring '08 term at Trinity University.

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chapter3(7) - MATH1010 Chapter 3 cont and Chapter 4 1...

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