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2. Consider the function t) = fl e'zg dz for 0 S t g 1. [I (3) Find both the Lagrange and Newton forms of the iterpolating polynomial p2(t) that interpolates t) at t = U. 0.5 and 1. Use SciPy's erf function scipy-special-erf to determine the value we of t) at each interpolation node ti, but don't forget to note that f(t) = ? -erf(t). (b) Write both polynomials in the form 61 + Cgtl + c3t2 and verify that the Lagrange and Newton techniques determined the same polynomial. Dept. of Computer Science, University of Toronto. St. George Campus Page 1 of 2 030 335 H1F ASSIGNMENT THREE Fall 2020 (c) Next calculate an approximation to f (0.336) by evaluating the interpolant p; at t = 0.335. Determine the absolute error in the apprmcimation. ((1) Determine a good upper bound for the error in approximating f(t) by p2(t) on the interval [0, 1]. Use Heath's upper bound result found on pg. 324. Is the absolute error computed in Part (c) consistent with this bound