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 Ti(x), T3(x), T5(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 Ti(x), T3(x), T5(x), and T7(x), all on the same graph, with domain x (-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 = np.sinh(x) plt.plot(x,11, label='$T_1(x)$') plt.plot(x,T3, label='$T_3(x)$') plt.plot(x, T5, label='$T_5(x)$') plt.plot(x,T7, label='$T_7(x)$') 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 T1, T3, T5 and T7 the appropriate Taylor polynomials. Recall that in python, exponents are written as **, for instance x is written as X**5, and if you want to calculate the factorial of a number, say 3!, this can be done as math. factorial(3)