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Consider the function f(x)=exp(x). Let p=P₂ be the interpolation polynomial for the data x=(0,1/2,1) and y=(exp(0),exp(1/2),exp(1)). Determine the value = ['₁ S = O a. s=0.179 O b. s-0.197 O c. S=0.719 O d. s-0.791 O e. s=0.971 O f. s 1.179 Og. s=1.197 Oh. s-1.719 O i. S=1.791 Oj. s=1.971 p(x)dx up to the third digit behind the point. Hint: You can compute the desired value brute force. Alternatively, you can go back to the lecture notes and identify where this construction occurs, and which simple formula gives the desired value.

Consider the function f(x)=exp(x). Let p=P₂ be the interpolation polynomial for the data x=(0,1/2,1) and y=(exp(0),exp(1/2),exp(1)). Determine the value = ['₁ S = O a. s=0.179 O b. s-0.197 O c. S=0.719 O d. s-0.791 O e. s=0.971 O f. s 1.179 Og. s=1.197 Oh. s-1.719 O i. S=1.791 Oj. s=1.971 p(x)dx up to the third digit behind the point. Hint: You can compute the desired value brute force. Alternatively, you can go back to the lecture notes and identify where this construction occurs, and which simple formula gives the desired value.

Advanced Engineering Mathematics
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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Consider the function f(x)=exp(x). Let p=P₂ be the interpolation polynomial for the data x=(0,1/2,1) and y=(exp(0),exp(1/2),exp(1)). Determine the value a. s=0.179 O b. s-0.197 C. up to the third digit behind the point. Hint: You can compute the desired value brute force. Alternatively, you can go back to the lecture notes and identify where this construction occurs, and which simple formula gives the desired value. O d. s=0.791 e. O f. s=0.719 s=0.971 O i. O j. s=1.179 g. s=1.197 h. s=1.719 1 = [" s=1.791 s=1.971 S = p(x)dx
Transcribed Image Text:Consider the function f(x)=exp(x). Let p=P₂ be the interpolation polynomial for the data x=(0,1/2,1) and y=(exp(0),exp(1/2),exp(1)). Determine the value a. s=0.179 O b. s-0.197 C. up to the third digit behind the point. Hint: You can compute the desired value brute force. Alternatively, you can go back to the lecture notes and identify where this construction occurs, and which simple formula gives the desired value. O d. s=0.791 e. O f. s=0.719 s=0.971 O i. O j. s=1.179 g. s=1.197 h. s=1.719 1 = [" s=1.791 s=1.971 S = p(x)dx
Expert Solution
Step 1

Given data set is as follows x=(0,1/2,1) and y=e0,e1/2,e1.

To Find: The value of s=∫01pdx where p∈P2 be an interpolation variable.

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