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Write out the Taylor series expansion of the function f(x) = /1+x about x = 0, up to the 2nd order. %3D (i) Using a plotting program such as Matlab or Mathematica, plot both the original func- tion, f(x) = /1+I , and the truncated Taylor series expansion. Restrict the x-range on your plot to values between -1.0 and 1.0. (ii) Calculate the definite integral (to 6-decimal precision): c0.25 VI+x dx (1) (iii) Calculate the definite integral (to 6-decimal precision) of the truncated Taylor series expansion, using the same limits of integration.

Write out the Taylor series expansion of the function f(x) = /1+x about x = 0, up to the 2nd order. %3D (i) Using a plotting program such as Matlab or Mathematica, plot both the original func- tion, f(x) = /1+I , and the truncated Taylor series expansion. Restrict the x-range on your plot to values between -1.0 and 1.0. (ii) Calculate the definite integral (to 6-decimal precision): c0.25 VI+x dx (1) (iii) Calculate the definite integral (to 6-decimal precision) of the truncated Taylor series expansion, using the same limits of integration.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Write out the Taylor series expansion of the function f(x) = /1+x about x = 0, up to the 2nd order. (i) Using a plotting program such as Matlab or Mathematica, plot both the original func- tion, f(x) on your plot to values between -1.0 and 1.0. (ii) Calculate the definite integral (to 6-decimal precision): V1+x , and the truncated Taylor series expansion. Restrict the x-range c0.25 VI+a dr (1) -0.25 (iii) Calculate the definite integral (to 6-decimal precision) of the truncated Taylor series expansion, using the same limits of integration.
Transcribed Image Text:Write out the Taylor series expansion of the function f(x) = /1+x about x = 0, up to the 2nd order. (i) Using a plotting program such as Matlab or Mathematica, plot both the original func- tion, f(x) on your plot to values between -1.0 and 1.0. (ii) Calculate the definite integral (to 6-decimal precision): V1+x , and the truncated Taylor series expansion. Restrict the x-range c0.25 VI+a dr (1) -0.25 (iii) Calculate the definite integral (to 6-decimal precision) of the truncated Taylor series expansion, using the same limits of integration.
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