The Taylor-series expansion around zero (Maclaurin Series) for sin(x) can be written as follows: 00 sin(x)...

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The Taylor-series expansion around zero (Maclaurin Series) for sin(x) can be written as follows: 00 sin(x) = x²0+1 a) Write a Python function that generates the first 10 terms of the sin(x) Taylor-series expansion around zero. b) Create a plot (or a series of plots) that compares sin(x) with its Taylor series for [1,2,3,10] terms. (You can use a sampled x vector that goes from -10 to +10, on steps of 100). c) Plot ex and the first 10 real and imaginary terms of its Taylor series expansion near x = 0, where the Taylor expansion at 0 can be written as follows: (-1)" (2n)! (-1)" (2n+1)! (n)! #... n=0 x" = Σ n=() #... (-1)" (2n + 1)! n=0 where j2n = (j²)" = (-1)" and j2n+1 = j(j2)" =j(-1)". This should be a 3D plot with x on the x-axis, cos(x) on the y-axis and sin(x) on the z-axis. Hint for 3D plotting: plt3D.legend () plt.show() # get 3D plot area to plot on plt 3D plt.figure().add_subplot (111, projection='3d') #call plot functions with plt3D. instead of plt. #Note: plt3D is an "axis" object and its API uses #set_XXX for axis labels and limits where the pyplot API # would use just XXX. Example: plt.xlim() -> plt3D.set_xlim() + Σ -x-²0+1 7=() #make the plot plt3D.plot(x, y, z) # where x,y,z are what you want to plot #p1t3D.set_xlabel (<text>) #plt3D.set_xlim (xmin, xmax) = cos(x) + jsin(x) Act Go t The Taylor-series expansion around zero (Maclaurin Series) for sin(x) can be written as follows: 00 sin(x) = x²0+1 a) Write a Python function that generates the first 10 terms of the sin(x) Taylor-series expansion around zero. b) Create a plot (or a series of plots) that compares sin(x) with its Taylor series for [1,2,3,10] terms. (You can use a sampled x vector that goes from -10 to +10, on steps of 100). c) Plot ex and the first 10 real and imaginary terms of its Taylor series expansion near x = 0, where the Taylor expansion at 0 can be written as follows: (-1)" (2n)! (-1)" (2n+1)! (n)! #... n=0 x" = Σ n=() #... (-1)" (2n + 1)! n=0 where j2n = (j²)" = (-1)" and j2n+1 = j(j2)" =j(-1)". This should be a 3D plot with x on the x-axis, cos(x) on the y-axis and sin(x) on the z-axis. Hint for 3D plotting: plt3D.legend () plt.show() # get 3D plot area to plot on plt 3D plt.figure().add_subplot (111, projection='3d') #call plot functions with plt3D. instead of plt. #Note: plt3D is an "axis" object and its API uses #set_XXX for axis labels and limits where the pyplot API # would use just XXX. Example: plt.xlim() -> plt3D.set_xlim() + Σ -x-²0+1 7=() #make the plot plt3D.plot(x, y, z) # where x,y,z are what you want to plot #p1t3D.set_xlabel (<text>) #plt3D.set_xlim (xmin, xmax) = cos(x) + jsin(x) Act Go t

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a Python function to generate the first 10 terms of the sinx Taylor series import math def sintaylor... View the full answer