1) Please be advised that you will asked to use a stopping criterion of the form |f(PN) <6, which we have not used so far in the homework assignments. One of the advantages of such an stopping criterion is that users of scientific calculators will be able to use it 'on the fly; however, among the disadvantages may be inability of some models of sci calculators to produce sufficiently accurate values of functions (if this will turn out to be the case, try to procure a better calculator, or to solve the problem using programming). 2) Do practice the method with a scientific calculator (at the very least, it may turn handy during the final exams). As was discussed in class, you can use the following program for a scientific calculator. a → X b➡Y f(x) → E (1) f(Y) F Y FX (Y-X) (F-E) C f(C) → D X C Y (2) D (4+) (3) No EX DO C → X DE Yes C→ Y D→ F (4-) Recall that the terms d... Pb, and f(p.) are kept in the variables X, C, Y, and D, respectively. The sign of the product f(a.)/(p.) is determined upon the execution of the command in Block (3). (Regula Falsi Method). All numerical answers should be rounded to 6-digit floating-point numbers. Use the Regula Falsi Method to find an approximation py of the root p of the function in [0.06, 0.09] satisfying f(x) - 2 sin + 0.06086 \(PN)|< 10-5. Show your work by filling in the following output table. As with the Bisection method, please enter appropriate letter signs +,- in the column labelled by f(a.) f(p); do NOT enter numbers in this column! Don't forget to drop leading minuses before entering numbers in the last column (in which the non-negative values (p.) should be entered). Enter asterisks in any unnecessary input fields. n an 2 3 4 5 6 7 Accordingly, PN= Check Pa bn f(an)f(pa) |f(pa)|
1) Please be advised that you will asked to use a stopping criterion of the form |f(PN) <6, which we have not used so far in the homework assignments. One of the advantages of such an stopping criterion is that users of scientific calculators will be able to use it 'on the fly; however, among the disadvantages may be inability of some models of sci calculators to produce sufficiently accurate values of functions (if this will turn out to be the case, try to procure a better calculator, or to solve the problem using programming). 2) Do practice the method with a scientific calculator (at the very least, it may turn handy during the final exams). As was discussed in class, you can use the following program for a scientific calculator. a → X b➡Y f(x) → E (1) f(Y) F Y FX (Y-X) (F-E) C f(C) → D X C Y (2) D (4+) (3) No EX DO C → X DE Yes C→ Y D→ F (4-) Recall that the terms d... Pb, and f(p.) are kept in the variables X, C, Y, and D, respectively. The sign of the product f(a.)/(p.) is determined upon the execution of the command in Block (3). (Regula Falsi Method). All numerical answers should be rounded to 6-digit floating-point numbers. Use the Regula Falsi Method to find an approximation py of the root p of the function in [0.06, 0.09] satisfying f(x) - 2 sin + 0.06086 \(PN)|< 10-5. Show your work by filling in the following output table. As with the Bisection method, please enter appropriate letter signs +,- in the column labelled by f(a.) f(p); do NOT enter numbers in this column! Don't forget to drop leading minuses before entering numbers in the last column (in which the non-negative values (p.) should be entered). Enter asterisks in any unnecessary input fields. n an 2 3 4 5 6 7 Accordingly, PN= Check Pa bn f(an)f(pa) |f(pa)|
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
![1) Please be advised that you will asked to use a stopping criterion of the form
|f(PN) <6,
which we have not used so far in the homework assignments. One of the advantages of such an stopping criterion is that users of scientific calculators will be able to use it 'on
the fly; however, among the disadvantages may be inability of some models of sci calculators to produce sufficiently accurate values of functions (if this will turn out to be the
case, try to procure a better calculator, or to solve the problem using programming).
2) Do practice the method with a scientific calculator (at the very least, it may turn handy during the final exams). As was discussed in class, you can use the following program
for a scientific calculator.
a → X
b➡Y
f(x) → E
(1)
f(Y)
F
Y FX (Y-X) (F-E) C
f(C) → D
<Rcl> X
<Rcl> C
<Rcl> Y
(2)
<Rcl> D
(4+)
(3)
No
EX DO
C → X
DE
Yes
C→ Y
D→ F
(4-)
Recall that the terms d... Pb, and f(p.) are kept in the variables X, C, Y, and D, respectively. The sign of the product f(a.)/(p.) is determined upon the execution of the
command in Block (3).
(Regula Falsi Method). All numerical answers should be rounded to 6-digit floating-point numbers.
Use the Regula Falsi Method to find an approximation py of the root p of the function
in [0.06, 0.09] satisfying
f(x)
- 2 sin
+ 0.06086
\(PN)|< 10-5.
Show your work by filling in the following output table.
As with the Bisection method, please enter appropriate letter signs +,- in the column labelled by f(a.) f(p); do NOT enter numbers in this column!
Don't forget to drop leading minuses before entering numbers in the last column (in which the non-negative values (p.) should be entered).
Enter asterisks in any unnecessary input fields.
n
an
2
3
4
5
6
7
Accordingly,
PN=
Check
Pa
bn
f(an)f(pa)
|f(pa)|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3361ca50-fe39-4902-8c9b-25c25195dd96%2F4939cb13-a18c-4c54-8ec2-5bab68002a42%2Foxb6dcb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1) Please be advised that you will asked to use a stopping criterion of the form
|f(PN) <6,
which we have not used so far in the homework assignments. One of the advantages of such an stopping criterion is that users of scientific calculators will be able to use it 'on
the fly; however, among the disadvantages may be inability of some models of sci calculators to produce sufficiently accurate values of functions (if this will turn out to be the
case, try to procure a better calculator, or to solve the problem using programming).
2) Do practice the method with a scientific calculator (at the very least, it may turn handy during the final exams). As was discussed in class, you can use the following program
for a scientific calculator.
a → X
b➡Y
f(x) → E
(1)
f(Y)
F
Y FX (Y-X) (F-E) C
f(C) → D
<Rcl> X
<Rcl> C
<Rcl> Y
(2)
<Rcl> D
(4+)
(3)
No
EX DO
C → X
DE
Yes
C→ Y
D→ F
(4-)
Recall that the terms d... Pb, and f(p.) are kept in the variables X, C, Y, and D, respectively. The sign of the product f(a.)/(p.) is determined upon the execution of the
command in Block (3).
(Regula Falsi Method). All numerical answers should be rounded to 6-digit floating-point numbers.
Use the Regula Falsi Method to find an approximation py of the root p of the function
in [0.06, 0.09] satisfying
f(x)
- 2 sin
+ 0.06086
\(PN)|< 10-5.
Show your work by filling in the following output table.
As with the Bisection method, please enter appropriate letter signs +,- in the column labelled by f(a.) f(p); do NOT enter numbers in this column!
Don't forget to drop leading minuses before entering numbers in the last column (in which the non-negative values (p.) should be entered).
Enter asterisks in any unnecessary input fields.
n
an
2
3
4
5
6
7
Accordingly,
PN=
Check
Pa
bn
f(an)f(pa)
|f(pa)|
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