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2.8.3 (Calibrating the Euler method) The goal of this problem is to test the Euler method on the initial value problem x =-x , x(0) = 1. a) Solve the problem analytically. What is the exact value of x(1)? b) Using the Euler method with step size Δ 1, estimate x(1) numerically-call the result$(1). Then repeat, using Δ1-10, for n = 1, 2, 3, 4. c) Plot the error E =|f(l)-x() as a function of Δ. Then plot In E vs. In t. Explain the results.

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a) t4C--ㄧㄧㄣ 2 e.0了 Σ.On methodto Teun mdliod 더 X(0.2) 0.9abau pottan

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