When S = 9 1. Iterate towards a root of the function A(x) using the Newton's method and the initial value x₁=¹75. Present two iterations to solve x₂ with the first iteration including all hand 25 calculations. Also present the values of the function and its derivative for the two iteration steps. Solve and present x₂ with the accuracy of three significant numbers.
When S = 9 1. Iterate towards a root of the function A(x) using the Newton's method and the initial value x₁=¹75. Present two iterations to solve x₂ with the first iteration including all hand 25 calculations. Also present the values of the function and its derivative for the two iteration steps. Solve and present x₂ with the accuracy of three significant numbers.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
The function for A(x), B(x),and C(x,y) are below.
S = 9
![Personal study question
When S = 9
1. Iterate towards a root of the function A(x) using the Newton's method and the initial
value x₁=¹75. Present two iterations to solve x₂ with the first iteration including all hand
25
calculations. Also present the values of the function and its derivative for the two iteration steps.
Solve and present x₂ with the accuracy of three significant numbers.
2.Iterate towards an extreme value of the function B(x) using the Newton's method and the
initial value Xo = -2.2- S/4. Present two iterations to solve x₂ with the first iteration including all
hand calculations. Also present the values of the function and its derivative for the two iteration
steps. Finally, show how close to the actual root you could reach with the accuracy of three
significant numbers. Please use a mathematical software or calculator to identify the sufficiently
accurate root.
17-S
25 }
17-S
25
3. Iterate towards a maximum value of the function C(x, y) using the Newton's method with fixed
step and the initial value [xo.Yo] = [3+ 4-
Present one iteration to solve [X₁, Y₁]
including all hand calculations. Also, please present the function C(x,y) value for all iterations.
Present [x₁, y₁ ] and C(x₁, y₁) with the accuracy of three significant numbers.
4.Iterate towards a minimum value of the function A(x) using the Golden Section algorithm. Use
12
the initial gap of [-(+25)
Calculate two iterations. Present all the observed values
(also d), rejected values, values of function, and your best point.
5.. Iterate towards an extreme value of the function B(x) using the quadratic interpolation. Use
the initial values x0 = -2.2- S/4, x₁ = 0, x₂ = 8. Calculate three iterations. Present all the
observed values, rejected values and your best point.
function:
S+
A(x) = 5 cos((¹+25) x n) +
12
B(x)=ex/2 +
S+2
9
-X
C(x,y)=-3x² +5x -(12-S)y²-2y +7xy](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3623d3da-044b-4b73-bcc0-32ece78b7acc%2Fe366d498-24e7-4dd9-8cbe-3c311a740c1b%2Ftr88g2ot_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Personal study question
When S = 9
1. Iterate towards a root of the function A(x) using the Newton's method and the initial
value x₁=¹75. Present two iterations to solve x₂ with the first iteration including all hand
25
calculations. Also present the values of the function and its derivative for the two iteration steps.
Solve and present x₂ with the accuracy of three significant numbers.
2.Iterate towards an extreme value of the function B(x) using the Newton's method and the
initial value Xo = -2.2- S/4. Present two iterations to solve x₂ with the first iteration including all
hand calculations. Also present the values of the function and its derivative for the two iteration
steps. Finally, show how close to the actual root you could reach with the accuracy of three
significant numbers. Please use a mathematical software or calculator to identify the sufficiently
accurate root.
17-S
25 }
17-S
25
3. Iterate towards a maximum value of the function C(x, y) using the Newton's method with fixed
step and the initial value [xo.Yo] = [3+ 4-
Present one iteration to solve [X₁, Y₁]
including all hand calculations. Also, please present the function C(x,y) value for all iterations.
Present [x₁, y₁ ] and C(x₁, y₁) with the accuracy of three significant numbers.
4.Iterate towards a minimum value of the function A(x) using the Golden Section algorithm. Use
12
the initial gap of [-(+25)
Calculate two iterations. Present all the observed values
(also d), rejected values, values of function, and your best point.
5.. Iterate towards an extreme value of the function B(x) using the quadratic interpolation. Use
the initial values x0 = -2.2- S/4, x₁ = 0, x₂ = 8. Calculate three iterations. Present all the
observed values, rejected values and your best point.
function:
S+
A(x) = 5 cos((¹+25) x n) +
12
B(x)=ex/2 +
S+2
9
-X
C(x,y)=-3x² +5x -(12-S)y²-2y +7xy
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