Given the function: f(x) = In (3x + 1) 1. Write the Taylor series centered at...

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Given the function: f(x) = In (3x + 1) 1. Write the Taylor series centered at zero for the function f(r). Write a program to plot the exact function and the Taylor series approximation on z € [0.0.5] using 2 and 5 terms. For the plots use Az = 0.001. Explain your results. 2. Write a program that computes the L2-norm of the error vector that results from the difference between the approximated and the exact values on the specified interval r. Compute the norm using 2 and 5 terms. Explain the differences. Given the function: f(x) = In (3x + 1) 1. Write the Taylor series centered at zero for the function f(r). Write a program to plot the exact function and the Taylor series approximation on z € [0.0.5] using 2 and 5 terms. For the plots use Az = 0.001. Explain your results. 2. Write a program that computes the L2-norm of the error vector that results from the difference between the approximated and the exact values on the specified interval r. Compute the norm using 2 and 5 terms. Explain the differences.