UFCalcSet21 - Exercises UF Calculus Set 21 1. Examine the...

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Exercises UF Calculus Set 21 1. Examine the graph of f ( x ) shown. Around which points would the linearizations seem to be the least accurate for small changes in x ? Where would it seem to be most accurate? What feature of f seems to determine this? (Note: we will soon see that this feature can be studied with the second derivative, which is why it is prominent in our error formula.) 2. Write the linearization of the function at the points indicated. Sketch the function and the two linearizations on the same axes, and answer the question provided. (a) f ( x ) = ln( x ) at (1 , 0) and ( e, 1) ; which gives the better approximation for ln(2) ? (b) f ( x ) = e x at (0 , 1) and (1 ,e ) ; which gives the better approximation for e ? (c) f ( x ) = 1 + x at (0 , 1) and (3 , 2) ; which gives the better approximation for 3 ? 3. For each of the functions below, write the differential, and calculate dy for the given values of x and dx . How accurate is dy in approximating Δ y (what is their difference) to the nearest
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UFCalcSet21 - Exercises UF Calculus Set 21 1. Examine the...

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