2. (Recursively Defined Sequences). (i) Study the following program for a scientific calculator for calculating the terms of the sequence (Pn) recursively defined by Pn=Pn-1-f(pn-1) Pn-1-Pn-2 f(pn-1)-f(pn-2) for all n > 2, where Po 1 and p₁=0.8 and where the function f is given by f(x) = sin(0.57x) - 0.28 (replace po and pi in the program with the corresponding values given above, and replace f(x) and f(Y) with correct expressions representing the values of the function f given above; say, f (x) should be replaced with Ixsin (0.57 x X ) - 0.28 Po X PLY f(X) E f(Y) F Y Fx (Y-X) + (F-E) → C Y→ X FE C→ Y (1) n (3) Prior to studying the above program, it is a good idea to start with creating your own program for calculating the terms p, in a familiar programming language, and/or in Excel (OpenOffice), and then to compare your program with the program for a sci calculator. 0 1 2 (ii) Execute the program for a sci calculator to get the terms P2, P3, Pio of the sequence (p₁) (make sure that your calculator is in it RADIAN mode). Present the results of your calculations in a table of the form All terms p must be rounded to eight decimal places after the period. (2) Pn Po pi P2
2. (Recursively Defined Sequences). (i) Study the following program for a scientific calculator for calculating the terms of the sequence (Pn) recursively defined by Pn=Pn-1-f(pn-1) Pn-1-Pn-2 f(pn-1)-f(pn-2) for all n > 2, where Po 1 and p₁=0.8 and where the function f is given by f(x) = sin(0.57x) - 0.28 (replace po and pi in the program with the corresponding values given above, and replace f(x) and f(Y) with correct expressions representing the values of the function f given above; say, f (x) should be replaced with Ixsin (0.57 x X ) - 0.28 Po X PLY f(X) E f(Y) F Y Fx (Y-X) + (F-E) → C Y→ X FE C→ Y (1) n (3) Prior to studying the above program, it is a good idea to start with creating your own program for calculating the terms p, in a familiar programming language, and/or in Excel (OpenOffice), and then to compare your program with the program for a sci calculator. 0 1 2 (ii) Execute the program for a sci calculator to get the terms P2, P3, Pio of the sequence (p₁) (make sure that your calculator is in it RADIAN mode). Present the results of your calculations in a table of the form All terms p must be rounded to eight decimal places after the period. (2) Pn Po pi P2
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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![2. (Recursively Defined Sequences). (i) Study the following program for a scientific calculator for calculating the terms of the sequence
(Pn) recursively defined by
PnPn-1-f(p-1)-
for all n>2, where
Po= 1 and p₁=0.8
and where the function f is given by
f(x) = sin(0.57x) - 0.28
(replace po and pi in the program with the corresponding values given above, and replace f(x) and f(Y) with correct expressions
representing the values of the function f given above; say, f (x) should be replaced with
Xxsin (0.57 x X ) - 0.28
Po X
PLY
f(x)→ E
Y→ X
F→ E
C→ Y
f(Y) → F
Y FX (Y-X) + (F-E) → C
Pn-1-Pn-2
f(pn-1)-f(pn-2)
(1)
n
(3)
0
1
2
Prior to studying the above program, it is a good idea to start with creating your own program for calculating the terms p, in a familiar
programming language, and/or in Excel (OpenOffice), and then to compare your program with the program for a sci calculator.
(ii) Execute the program for a sci calculator to get the terms P2, P3,
in it RADIAN mode). Present the results of your calculations in a table of the form
(2)
Pn
Po
P₁
P2
Pio of the sequence (P₁) (make sure that your calculator is
All terms p must be rounded to eight decimal places after the period.
(iii) It can be shown that in fact the sequence (p), generated by the so-called Secant Method for root finding problems, converges to
the unique root y of the function f in [0,1]. With this in mind, use the WolframAlpha (Wa) website to find the 10-digit approximation
of y by executing the command
solve x+sin( 0.57x)=0.28 in [0,1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc899b398-58b7-4cf1-b7ff-d9a6ccf14417%2F4f13e9e6-17a6-4f8c-a370-1dc81b6c6bd7%2Frhten0k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. (Recursively Defined Sequences). (i) Study the following program for a scientific calculator for calculating the terms of the sequence
(Pn) recursively defined by
PnPn-1-f(p-1)-
for all n>2, where
Po= 1 and p₁=0.8
and where the function f is given by
f(x) = sin(0.57x) - 0.28
(replace po and pi in the program with the corresponding values given above, and replace f(x) and f(Y) with correct expressions
representing the values of the function f given above; say, f (x) should be replaced with
Xxsin (0.57 x X ) - 0.28
Po X
PLY
f(x)→ E
Y→ X
F→ E
C→ Y
f(Y) → F
Y FX (Y-X) + (F-E) → C
Pn-1-Pn-2
f(pn-1)-f(pn-2)
(1)
n
(3)
0
1
2
Prior to studying the above program, it is a good idea to start with creating your own program for calculating the terms p, in a familiar
programming language, and/or in Excel (OpenOffice), and then to compare your program with the program for a sci calculator.
(ii) Execute the program for a sci calculator to get the terms P2, P3,
in it RADIAN mode). Present the results of your calculations in a table of the form
(2)
Pn
Po
P₁
P2
Pio of the sequence (P₁) (make sure that your calculator is
All terms p must be rounded to eight decimal places after the period.
(iii) It can be shown that in fact the sequence (p), generated by the so-called Secant Method for root finding problems, converges to
the unique root y of the function f in [0,1]. With this in mind, use the WolframAlpha (Wa) website to find the 10-digit approximation
of y by executing the command
solve x+sin( 0.57x)=0.28 in [0,1]
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