Q3 (10 points) We want to examine how well various Taylor polynomials perform in approximating a function. We will use f(x) = sinh (x) and look at the Taylor expansion about x = 0. Calculate the Taylor polynomials T(x), T3(x), Ts(x), and T7(x) of f(x) = sinh x at x = 0. Then, using a computer algebra system, plot f(x), along with the Taylor polynomials T(x), 7)(x), 7(x), and T-(x), all on the same graph, with domain x E -5,5), so that you can readily see where each polynomial starts to deviate. NOTE: You can use your favourite computer algebra system. But if you do not know what to use, you can simply plot the graphs on python. Go to https://ualberta.syzygy.ca, sign in with your University of Alberta account, and open a jupyter notebook. To plot a graph as suggested above, the following python code should do: from matplotlib import pyplot as plt import numpy as np import math x = np.arange(-5, 5, 0.05) T1 = T3 = T5 - T7 = Y = ne-sinh (x) plt.plot(x,Ti, label='ST_1(x)$') plt.plot(x,T3, label='ST_3(x) $') plt.plot(x,15, label='ST_5(X)*') plt.plot(x,17, label-'ST_7(x) $') plt.plot(x,y,label='$\sinh(x) $') plt.legend (loc="upper left") plt.show() Here, you should enter on the right-hand-side of the equalities for T2, T3, T5 and 17 the appropriate Taylor polynomials. Recall that in python, exponents are written as .., for instance is written as x 5, and if you want to calculate the factorial of a number, say 31, this can be done as math.factorial(3). + Drag and drop your images or click to browse