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ay Problem 3: Given = (x+y-1), y(0) = 1, defined over the interval (0, 3] with a step h-1. Answer questions (12, 13, 14, 15, and 16). dx 12) The estimated value of y(2) using Euler Method is: (A) 2 (B) S (C) 4 (D) None 13) The estimated value of y(1) using Modified (Improved) Euler Method is (B) 1.5 (C) 3.25 (A) 2.5 (D) None 14) Given the first three terms of Taylor's Series formula needed to find the value of y as yo-y+hy+(h/2) y". The value of y(2) is: (A) 3.5 (B) 2.5 (C) 4.5 (D) None 15) Using 4 order Rung-Kutta method, the value of K₂ needed to evaluate y(1) is (A) 0.75 (B) 0.5 (C) 1 (D) None 16) the value of yo" is: (A) 3 (B) 1 (C) 4 (D) None

ay Problem 3: Given = (x+y-1), y(0) = 1, defined over the interval (0, 3] with a step h-1. Answer questions (12, 13, 14, 15, and 16). dx 12) The estimated value of y(2) using Euler Method is: (A) 2 (B) S (C) 4 (D) None 13) The estimated value of y(1) using Modified (Improved) Euler Method is (B) 1.5 (C) 3.25 (A) 2.5 (D) None 14) Given the first three terms of Taylor's Series formula needed to find the value of y as yo-y+hy+(h/2) y". The value of y(2) is: (A) 3.5 (B) 2.5 (C) 4.5 (D) None 15) Using 4 order Rung-Kutta method, the value of K₂ needed to evaluate y(1) is (A) 0.75 (B) 0.5 (C) 1 (D) None 16) the value of yo" is: (A) 3 (B) 1 (C) 4 (D) None

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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9) If the interval [0, 9] was divided into four points including (0, f(0)), (9, f (9)), the estimated area under f(x) between [0, 9] using Simpson's 1/3 Rule then Trapezoidal Rule is: (A) 1289 (B) 1358 (C) 1566 (D) None 10) If the step (h)-0.5 for the interval [0, 9], then by using Trapezoidal, the number of data points needed to evaluate the area of f(x) between [0, 9] is: (A) 30 (B) 31 (C) 19 (D) None 11) If the interval [0, 9] was divided into seven points including (0, f(0)), (9, F(9)). the area under f(x) between [0, 6] can't be evaluated using only: (A) Simpson's 3/8 (B) Simpson's 1/3 (C) Trapezoidal (D) None ay Problem 3: Given = (x + y - 1), y(0) = 1, defined over the interval (0, 3) with a step h-1. Answer questions (12, 13, 14, 15, and 16). dx 12) The estimated value of y(2) using Euler Method is: (A) 2 (B) S (C) 4 (D) None 13) The estimated value of y(1) using Modified (Improved) Euler Method is (B) 1.5 (A) 2.5 (C) 3.25 (D) None 14) Given the first three terms of Taylor's Series formula needed to find the value of y as yo-y₁+hy+(h/2) y". The value of y(2) is: (A) 3.5 (B) 2.5 (C) 4. S (D) None 15) Using 4 order Rung-Kutta method, the value of K₂ needed to evaluate y(1) is (A) 0.75 (B) 0.5 (C) 1 (D) None 16) the value of yo" is: (A) 3 (D) None Problem 4: Use the following set of equations to answer questions (17, 18, 19, 20, 21, and 22) (A) x₁ = 1 17) According to the iterative methods, the equation that is used to find the value of x is: 4 5 2 1 (C) x₁=5 (B) 1 X2 X₂ 6x₁- 8x₂ = 1 4x₁ + 3x₂ = 2 (1) (2) (B) x₁ => (D) None 18) If (x,x))-(1, 2). The value of x) by Jacobi is: (A) -5/6 (B)-4/3 (C)-3/8 (D) None
Transcribed Image Text:9) If the interval [0, 9] was divided into four points including (0, f(0)), (9, f (9)), the estimated area under f(x) between [0, 9] using Simpson's 1/3 Rule then Trapezoidal Rule is: (A) 1289 (B) 1358 (C) 1566 (D) None 10) If the step (h)-0.5 for the interval [0, 9], then by using Trapezoidal, the number of data points needed to evaluate the area of f(x) between [0, 9] is: (A) 30 (B) 31 (C) 19 (D) None 11) If the interval [0, 9] was divided into seven points including (0, f(0)), (9, F(9)). the area under f(x) between [0, 6] can't be evaluated using only: (A) Simpson's 3/8 (B) Simpson's 1/3 (C) Trapezoidal (D) None ay Problem 3: Given = (x + y - 1), y(0) = 1, defined over the interval (0, 3) with a step h-1. Answer questions (12, 13, 14, 15, and 16). dx 12) The estimated value of y(2) using Euler Method is: (A) 2 (B) S (C) 4 (D) None 13) The estimated value of y(1) using Modified (Improved) Euler Method is (B) 1.5 (A) 2.5 (C) 3.25 (D) None 14) Given the first three terms of Taylor's Series formula needed to find the value of y as yo-y₁+hy+(h/2) y". The value of y(2) is: (A) 3.5 (B) 2.5 (C) 4. S (D) None 15) Using 4 order Rung-Kutta method, the value of K₂ needed to evaluate y(1) is (A) 0.75 (B) 0.5 (C) 1 (D) None 16) the value of yo" is: (A) 3 (D) None Problem 4: Use the following set of equations to answer questions (17, 18, 19, 20, 21, and 22) (A) x₁ = 1 17) According to the iterative methods, the equation that is used to find the value of x is: 4 5 2 1 (C) x₁=5 (B) 1 X2 X₂ 6x₁- 8x₂ = 1 4x₁ + 3x₂ = 2 (1) (2) (B) x₁ => (D) None 18) If (x,x))-(1, 2). The value of x) by Jacobi is: (A) -5/6 (B)-4/3 (C)-3/8 (D) None
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