HW01.pdf - Math 104A Homework#1 Instructor Lihui Chai General Instructions Please write your homework papers neatly You need to turn in both full

# HW01.pdf - Math 104A Homework#1 Instructor Lihui Chai...

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Math 104A Homework #1 * Instructor: Lihui Chai General Instructions: Please write your homework papers neatly. You need to turn in both full printouts of your codes and the appropriate runs you made. Write your own code, individually. Do not copy codes! 1. Review and state the following theorems of Calculus (see for example 1.1 and 1.2 in thetextbook):(a) The Intermediate Value Theorem.(b) The Mean Value Theorem.(c) Rolles Theorem.(d) The Mean Value Theorem for Integrals.(e) The Weighted Mean Value Theorem for Integrals.2. Write a computer code to implement the Composite Trapezoidal Rule quadratureTh[f] =h12f(x0) +f(x1) +...+f(xN-1) +12f(xN),(1)to approximate the definite integralZbaf(x)dx,(2)using the equally spaced points