%matplotlib inlineimport numpy as npfrom matplotlib import pyplot as pltimport math Problem 22.1) Show that (you need to show that the error term is O(h²)).f'(x) =− f(x+2h)+4ƒ(x + h) −3f(x)+0(h²)2h12.2) Let fƒ(x) = xe. Use the formula in 4.1) to find the "first" derivative of f(x) and plot the first derivative for x = [0, 1]. Pick appropriate value for h.12.3) Let f(x)1=xe*. Use the formula in 4.2) to find the "second" derivative of f(x) and plot the second derivative for 2 € [0,1]

Question: For part 2.1, to show that the error term is O(h^2), we need to analyze the given formula…

Answered: Problem 2 2.1) Show that (you need to…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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%matplotlib inlineimport mathimport numpy as npfrom matplotlib import pyplot as pltdef bad_poisson(lmd, k): return pow(lmd,k)*math.exp(-lmd)/math.factorial(k)# bad_poisson(1000,1000) # uncomment to see it breaks
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1. Import NumPy as np
2. Problem 2: In this problem you will test our "in class" version of Gaussian elimination against the version in numpy. Use both codes to solve some randomly chosen linear systems of size N 10, 20, 40, 80, 160, 320, 640, 1280, 2560, and 5120. Depending on your computer, the last two may or may not work. If they don't, just say so in your report. If you computer can do N- 10240 then try this as well. Note that in cach case N 10 * 2k for k = 1,..., 10. That is, each time we are doubling the size of the matrix. abone Plot the results as two curves. Our code in red and numPy in bluc. (Or whatever colors you prefer). Can you guess the function which governs the runtime? Based on this guess, how long would it take to do N 40960 using numPy? N=81920?

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