Problem 2 Given the data set (Xg, Yk): Xo = 1; Xx = Xx-1 + 0.2 for k = 1 and 2; Y* =sin(2x,) a) Write down the 2nd order Lagrange polynomial constructed from the above data. Show the final result in the compact form: ax? + bx + c, where a,b, and c are to be determined.
Problem 2 Given the data set (Xg, Yk): Xo = 1; Xx = Xx-1 + 0.2 for k = 1 and 2; Y* =sin(2x,) a) Write down the 2nd order Lagrange polynomial constructed from the above data. Show the final result in the compact form: ax? + bx + c, where a,b, and c are to be determined.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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![Problem 2
Given the data set (Xg, Yk); Xo = 1;
Xg = Xg-1+ 0.2 for k = 1 and 2;
Yk =sin(2xx)
a) Write down the 2nd order Lagrange polynomial constructed from the above data. Show the final result in the
compact form: ax? + bx + c, where a, b, and c are to be determined.
b) Plot the obtained polynomial and the original function on the same graph over an interval [1, 1.4]. Use 0.01
increment while plotting the polynomial and original function.
c) Evaluate the error when the generated polynomial is evaluated at x = 1.3?
d) Compare the error obtained in part e with the error bound.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feffc0def-cbbe-433e-b1d5-a4a12f49f24b%2Fc691cbbb-a8c4-4f0c-975f-0c26ed35241f%2F3ngq7z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 2
Given the data set (Xg, Yk); Xo = 1;
Xg = Xg-1+ 0.2 for k = 1 and 2;
Yk =sin(2xx)
a) Write down the 2nd order Lagrange polynomial constructed from the above data. Show the final result in the
compact form: ax? + bx + c, where a, b, and c are to be determined.
b) Plot the obtained polynomial and the original function on the same graph over an interval [1, 1.4]. Use 0.01
increment while plotting the polynomial and original function.
c) Evaluate the error when the generated polynomial is evaluated at x = 1.3?
d) Compare the error obtained in part e with the error bound.
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