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              "value": "The appropriate choice of \"scale\" is a trade-off; too large and the function differs from its Taylor polynomial too much to get a good answer, too small and round-off errors overwhelm the higher-order terms. The algorithm used becomes numerically unstable around order 30 even under ideal circumstances."
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                      "value": "The Taylor polynomial (translated to the origin, so that for example p(0)=f(x))."
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        "value": "We can calculate Taylor approximation polynomials of sin function with\nvarious degrees:\n\n"
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        "value": "import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.interpolate import approximate_taylor_polynomial\nx = np.linspace(-10.0, 10.0, num=100)\n",
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