1. Consider y-f(x)=cos(2x)+x² over [0, 3t/2]. (By hand but use a calculator) a) Use the three nodes xo-0, x= 3n/4, x2= 3T/2 to construct a quadratic interpolation polynomial P2(x) and compare P2(1) and f(1). b) Use the three nodes xo=0, x= Tt/2, x2= T, X3= 37n/2 to construct a cubic interpolation polynomial P3(x) and compare P3(1) and f(1).
1. Consider y-f(x)=cos(2x)+x² over [0, 3t/2]. (By hand but use a calculator) a) Use the three nodes xo-0, x= 3n/4, x2= 3T/2 to construct a quadratic interpolation polynomial P2(x) and compare P2(1) and f(1). b) Use the three nodes xo=0, x= Tt/2, x2= T, X3= 37n/2 to construct a cubic interpolation polynomial P3(x) and compare P3(1) and f(1).
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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![1. Consider y-f(x)%3Dcos(2x)+x² over [0, 3t/2]. (By hand but use a calculator)
a) Use the three nodes xo-D0, x1= 3m/4, x2= 3t/2 to construct a quadratic interpolation
polynomial P2(x) and compare P2(1) and f(1).
b) Use the three nodes xg-D0, X= t/2, x2= T, x3= 37/2 to construct a cubic interpolation
polynomial P3(x) and compare P3(1) and f(1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4f1fee3-f58c-4ceb-984e-03f2977d10ad%2F00d49cf7-0a9f-4bc4-94b9-8087f4d79631%2Fuos3fr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider y-f(x)%3Dcos(2x)+x² over [0, 3t/2]. (By hand but use a calculator)
a) Use the three nodes xo-D0, x1= 3m/4, x2= 3t/2 to construct a quadratic interpolation
polynomial P2(x) and compare P2(1) and f(1).
b) Use the three nodes xg-D0, X= t/2, x2= T, x3= 37/2 to construct a cubic interpolation
polynomial P3(x) and compare P3(1) and f(1).
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