2.0Fit a cubic polynomial to the following data:35712y1.63.64.43.42,22.83.84.6

x y 3 1.6 4 3.6 5 4.4 7 3.4 8 2.2 9 2.8 11 3.8 12 4.6 cubic polynomial is of the…

Answered: 2.0 Fit a cubic polynomial to the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Fit a cubic polynomial to the following data: Using numerical methods, determine the coefficients, r2 and sy/x.
a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. f(x) = 8x³/2, a = 1; approximate 8(1.73/2) a. p₁(x) = b. p₂(x) = c. Using the linear approximating polynomial to estimate, 8 (1.73/2) is approximately (Simplify your answer.) Using the quadratic approximating polynomial to estimate, 8(1.73/2) is approximately. (Simplify your answer.)
A penny is thrown from the top of a 48.9-meter building and hits the ground 3.04 seconds after it was thrown. The penny reached its maximum height above the ground 0.79 seconds after it was thrown. Define a quadratic function, h, that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t. What is the maximum height of the penny above the ground?
6. 2. Quiz #7 Consider the following graph of a polynomial: -4 -2 4. 0. - -0- -20 Write the factored form of the equation of the most appropriate polynomial. Submit Assignr
Please show complete steps and solution, use excel or manual computation. 1. Find the Lagrange form of the interpolating polynomial for the following table of values: x| 1/3 | 1/4| 1 y 2 -1 7 2. Find the Newton form of the interpolating polynomial for the following table of values: x | 1/3 | 1/4 | 1 y|2 |-1 | 7 3. Construct a divided differences table and write out the Newton form of the interpolating polynomial for the following table of values: 1 | 3/2 | 0 | 2 f(x) 3 13/4 3 5/3 4. Given the data: 1.6 2 2.5 3.2 4.5 f(x) 14 15 2 Calculate f(2.8) using Newton's interpolating polynomials of order 1 through 3. Choose the sequence of the points for your estimates to attain the best possible accuracy.
2 For each of the following data, a polynomial fits the data exactly. Find the polynomial. 3 5 17 107 (a)* X y 1 −1 2 2 4 50 6 194

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2.0 Fit a cubic polynomial to the following data: 3 5 8 2.2 4 12 y 1.6 3.6 4.4 3.4 2.8 3.8 4.6