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A Taylor series is something we often use and looks like dy y(xo+h) = y(xo) +h(x) + h² d²y 2! dx² (x0) + where (ro) is the first derivative of y(x) evaluated at ro. Similarly (ro) is the second derivative of y(x) evaluated at xo and so on. If h is small, we can truncate this series and get a good local approximation to y(x) in the vicinity of o. Try the equation y(x) = 3x5 and set x = 3 and h = 0.05. Evaluate y at x = 3.05 by using the Taylor series truncated at the second (linear) and then the third (quadratic) term and compare with the actual answer.

A Taylor series is something we often use and looks like dy y(xo+h) = y(xo) +h(x) + h² d²y 2! dx² (x0) + where (ro) is the first derivative of y(x) evaluated at ro. Similarly (ro) is the second derivative of y(x) evaluated at xo and so on. If h is small, we can truncate this series and get a good local approximation to y(x) in the vicinity of o. Try the equation y(x) = 3x5 and set x = 3 and h = 0.05. Evaluate y at x = 3.05 by using the Taylor series truncated at the second (linear) and then the third (quadratic) term and compare with the actual answer.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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A Taylor series is something we often use and looks like dy y(xo+h) = y(xo) + (x) + dx h² d²y 2! dx² (x0) + where (ro) is the first derivative of y(x) evaluated at îo. Similarly (ro) is the second derivative of y(x) evaluated at ro and so on. If h is small, we can truncate this series and get a good local approximation to y(x) in the vicinity of xo. Try the equation y(x) = 3x5 and set x = 3 and h = 0.05. Evaluate y at x = 3.05 by using the Taylor series truncated at the second (linear) and then the third (quadratic) term and compare with the actual answer.
Transcribed Image Text:A Taylor series is something we often use and looks like dy y(xo+h) = y(xo) + (x) + dx h² d²y 2! dx² (x0) + where (ro) is the first derivative of y(x) evaluated at îo. Similarly (ro) is the second derivative of y(x) evaluated at ro and so on. If h is small, we can truncate this series and get a good local approximation to y(x) in the vicinity of xo. Try the equation y(x) = 3x5 and set x = 3 and h = 0.05. Evaluate y at x = 3.05 by using the Taylor series truncated at the second (linear) and then the third (quadratic) term and compare with the actual answer.
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