Problem 1: Given /(x) = 1 + x² + cos(x) that is defined over 10,41 with a step (h)-1. Solve points (1, 2, 3, 4, and 5) based on divided difference interpolation. 1) The value of the terms f[x, x3, x4] and f(x0, x1,x2, X3, X4 ] are respectively: (D) None (A)-1, 4/3 (B) 3, 2/3 (C) 3,-2/3 2) The maximum number of 3rd order polynomials we can get is: (A) 2 (B) 4 (C) 3 (D) None 3) the absolute error [P2(0.5)-f(0.5) is: (A) 2.5 (B) 0.5 4) Starting from (x-1), P:(1.5) is: (A) 3.5 (B) 2. 25 (C) 0.25 (C) 4.75 5) The first derivative of P2(x) at x-1 is: (A) 7 (B) 6 (C) 5 (D) None (D) None (D) None
Problem 1: Given /(x) = 1 + x² + cos(x) that is defined over 10,41 with a step (h)-1. Solve points (1, 2, 3, 4, and 5) based on divided difference interpolation. 1) The value of the terms f[x, x3, x4] and f(x0, x1,x2, X3, X4 ] are respectively: (D) None (A)-1, 4/3 (B) 3, 2/3 (C) 3,-2/3 2) The maximum number of 3rd order polynomials we can get is: (A) 2 (B) 4 (C) 3 (D) None 3) the absolute error [P2(0.5)-f(0.5) is: (A) 2.5 (B) 0.5 4) Starting from (x-1), P:(1.5) is: (A) 3.5 (B) 2. 25 (C) 0.25 (C) 4.75 5) The first derivative of P2(x) at x-1 is: (A) 7 (B) 6 (C) 5 (D) None (D) None (D) None
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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Problem 1
Solve Q4
![Problem 1: Given f(x) = 1 + x² + cos(x) that is defined over 10,41 with a step
(h)-1. Solve points (1, 2, 3, 4, and 5) based on divided difference interpolation.
1) The value of the terms f[x2, x3, x4] and f[x0, X1, X2, X3, X4] are respectively:
(D) None
(A)-1, 4/3 (B) 3, 2/3
(C) 3, -2/3
2) The maximum number of 3rd order polynomials we can get is:
(A) 2
(B) 4
(C) 3
(D) None
3) the absolute error P2(0.5) - (0.5)) is:
(A) 2.5
(B) 0.5
4) Starting from (x-1), P:(1.5) is:
(A) 3.5
(B) 2.25
(C) 0.25
5) The first derivative of P₂(x) at x=1 is:
(A) 7
(B) 6
(C) 5
6) P2(s) at x-0 is:
(A) 12
(C) 4.75
(B) 16
(D) None
Problem 2: Given f(x) = 1 + x² + cos(x) that is defined over 10,4] with a step
(h) = 1. Solve points (6, 7, 8, and 9) based on Difference table (N.G.F.).
(D) None
9) The second derivative of P3(s) at x=0 is:
(A) 10
(B) 14
(C) 23
(D) None
(C) 18
(D) None
7) Starting from (x-1), The second derivative of P2(s) at x-1 using central
derivative is:
(A) 6
(B)-2
(C)-8
(D) None
8) Starting from (x-1), the first derivative of P3(s) at x-1 is:
(A) 26/3
(B) 22/3
(C)-20/3
(D) None
(D) None](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c98319f-f7dd-43b6-afb0-8ac8c44bf313%2Fb932f070-d0d3-4831-805d-6c2824bf394d%2Fryqb99c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1: Given f(x) = 1 + x² + cos(x) that is defined over 10,41 with a step
(h)-1. Solve points (1, 2, 3, 4, and 5) based on divided difference interpolation.
1) The value of the terms f[x2, x3, x4] and f[x0, X1, X2, X3, X4] are respectively:
(D) None
(A)-1, 4/3 (B) 3, 2/3
(C) 3, -2/3
2) The maximum number of 3rd order polynomials we can get is:
(A) 2
(B) 4
(C) 3
(D) None
3) the absolute error P2(0.5) - (0.5)) is:
(A) 2.5
(B) 0.5
4) Starting from (x-1), P:(1.5) is:
(A) 3.5
(B) 2.25
(C) 0.25
5) The first derivative of P₂(x) at x=1 is:
(A) 7
(B) 6
(C) 5
6) P2(s) at x-0 is:
(A) 12
(C) 4.75
(B) 16
(D) None
Problem 2: Given f(x) = 1 + x² + cos(x) that is defined over 10,4] with a step
(h) = 1. Solve points (6, 7, 8, and 9) based on Difference table (N.G.F.).
(D) None
9) The second derivative of P3(s) at x=0 is:
(A) 10
(B) 14
(C) 23
(D) None
(C) 18
(D) None
7) Starting from (x-1), The second derivative of P2(s) at x-1 using central
derivative is:
(A) 6
(B)-2
(C)-8
(D) None
8) Starting from (x-1), the first derivative of P3(s) at x-1 is:
(A) 26/3
(B) 22/3
(C)-20/3
(D) None
(D) None
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