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In [1]: import numpy import matplotlib.pyplot as plt %matplotlib inline from time import time Problem 1: Using (-) sin(x) xljtl (2j +I) j-0 (Ipts) Derive Taylor series for sin(x) around x = 0. (3pts) Write a Python program which computes the Taylor series of sin(x) using recursion, non-vectorization, and tolerance-based while loop approach. (3pts) Write a Python program which computes the Taylor series of sin(x) using recursion, vectorization, and tolerance-based while loop approach. (Ipts) On the interval [0, #], plot the semi-log error in your approximation for tolerance values of 10^-5 using your Python program in (b). (Ipts) On the interval [0, x], plot the semi-log error in your approximation for tolerance values of 10^-5 using your Python program in (c). (Zpts) Compare the time it takes to run the Python program in (d) and (e). Which program takes longer to run and why?

          In [1]: import numpy
    import matplotlib.pyplot as plt
    %matplotlib inline
    
    from time import time
    
    Problem 1: Using
    
    (-) sin(x) xljtl (2j +I) j-0
    
    (Ipts) Derive Taylor series for sin(x) around x = 0.
    
    (3pts) Write a Python program which computes the Taylor series of sin(x) using recursion, non-vectorization, and tolerance-based while loop approach.
    
    (3pts) Write a Python program which computes the Taylor series of sin(x) using recursion, vectorization, and tolerance-based while loop approach.
    
    (Ipts) On the interval [0, #], plot the semi-log error in your approximation for tolerance values of 10^-5 using your Python program in (b).
    
    (Ipts) On the interval [0, x], plot the semi-log error in your approximation for tolerance values of 10^-5 using your Python program in (c).
    
    (Zpts) Compare the time it takes to run the Python program in (d) and (e). Which program takes longer to run and why?

in 1 import numpy import matplotlibpyplot as plt xmatplotlib inline from time import time problem 1 using sinx xljtl 2j i j 0 ipts derive taylor series for sinx around x 0 3pts write python 64286

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