The following function is given f(x) = ex [5] a) Expand the function at the expansion...

 

Transcribed Image Text:

The following function is given f(x) = ex [5] a) Expand the function at the expansion point xo = 1 using 3rd order Taylor series and evaluate its value at x=0.5. [5] b) Calculate the relative error. [10] c) State and prove the order of accuracy of the Taylor expansion. [20] d) Plot the function f(x) and its 3rd order Taylor series expansion at x0 = 1 in Matlab. Pay attention to the style (line thickness, symbols for data points) and format (legends, labeling) of the plot. The following function is given f(x) = ex [5] a) Expand the function at the expansion point xo = 1 using 3rd order Taylor series and evaluate its value at x=0.5. [5] b) Calculate the relative error. [10] c) State and prove the order of accuracy of the Taylor expansion. [20] d) Plot the function f(x) and its 3rd order Taylor series expansion at x0 = 1 in Matlab. Pay attention to the style (line thickness, symbols for data points) and format (legends, labeling) of the plot.