MAD4401Quiz2 - MAD 4401 Quiz 2 James Keesling 1 Numerical...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAD 4401 Quiz 2 James Keesling 1 Numerical Differentiation Problem 1.1. Determine a formula to estimate the third derivative of a function f (x) at the point x0 using the points {x0 − 3h, x0 − 2h, x0 − h, x0 , x0 + h, x0 + 2h, x0 + 3h}. Problem 1.2. In Problem 1.1 determine the optimal h in estimating the third derivative. Also determine the accuracy of the estimate assuming that the error in computing f (x) is approximately = 10−30 . Problem 1.3. Use the above to estimate the third derivative of sin(x) at x = 1. Of course, we can determine this exactly with the calculator without using the method. However, knowing the answer allows us to see exactly how accurate our method is. 2 Lagrange Interpolating Polynomials Problem 2.1. Determine the Lagrange polynomial approximating the function 1 1 + x2 over the interval [−4, 4] using equally spaced points, {−4 + for n = 10 and 20. Problem 2.2. Compare the graphs of the function in Problem 2.1. 3 1 1+x2 8·i n i = 0, 1, 2, . . . , n}. Do this and the two Lagrange polynomials Newton-Cotes Estimate of the Integral Problem 3.1. Determine the normalized Newton-Cotes coefficients for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Problem 3.2. Use the coefficients determined in Problem 3.1 to estimate the integral 4 −4 1 dx 1 + x2 for the given values of n. 1 ...
View Full Document

This note was uploaded on 11/12/2011 for the course STA 3032 taught by Professor Kyung during the Summer '08 term at University of Florida.

Ask a homework question - tutors are online