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Unformatted text preview: Lecture 21: Linear Approximations and Difierentials (Chapter 3, Sec. 21) We have seen that a curve y = f ( x ) closely follows its tangent line at a point ( a;f ( a )). That is, we can approximate a function value f ( x ) for x near a by the corresponding function value on the tangent line. Find the equation of the tangent line to y = f ( x ) at ( a;f ( a )): 6 ? The linearization of f at a is the linear function L ( x ) = 2 For xvalues near a , we note that This is the Tangent line or Linear approxima tion of f at a . ex. Find the linearization of f ( x ) = sin x at a = 0. Use it to approximate sin … 6 and sin … 10 . 3 ex. Find the linearization of f ( x ) = p x + 2 at a = 2, and use it to approximate p 3 : 96 and p 4 : 04. 6 ? 4 NOTE: The error in using L ( x ) to approximate f ( x ) is given by j L ( x ) ¡ f ( x ) j . In our example, we see that j L ( x ) ¡ f ( x ) j • : 000025 if j x ¡ 2 j • : 4....
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 Spring '08
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 Calculus, Geometry

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