Taylor polynomial

1- Consider f(x)=ln(1+x)

  1. a) Find the Taylor polynomial of degree three, p3(x), for f(x) centered at x 0=1.
  2. b) Maximize the absolute error bound for the Taylor polynomial approximation for 0.5≤x≤2.
  3. c) Calculate the absolute error at x =2. How is the error at x =2 compared to part (b).

2- Let f(x)=e^x+2x, 0≤x≤2.

  1. a) Find the Lagrange interpolating polynomial for the data x1=0and x2=2.
  2. b) Find the maximum error bound for the Lagrange Polynomial approximation for 0≤x≤2.


Last Updated on March 1, 2019

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