Suppose f(x) = 1/(1 + x) is to be approximated near x = 0. Find the linear
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Suppose f(x) = 1/(1 + x) is to be approximated near x = 0. Find the linear approximation to f at 0. Then complete the following table showing the errors in various approximations. Use a calculator to obtain the exact values. The percent error is 100|approximation - exact|/|exact|. Comment on the behavior of the errors as x approaches 0.
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Linear approx. Percent error Exact value х 0.1 0.01 0.001 0.0001 -0.0001 -0.001 -0.01 -0.1
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Note that fa f0 1 and fa 11 a 2 1 so the linear approximation has equation y Lx fa fax a 1 x Th...View the full answer
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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