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Open with Numerical method 8. (Note: This question does not ask you to implement the algorithm. You do the calculation manually. This question tests your understanding of the algorithm.) Refer to the Pseudocode for Bisection Method. Suppose we want to use this algorithm to find a root of f(x)3(x+1)(x-3), and we input tolerable error e = 0.0001. a. Among the following pairs of initial guesses for x0 and x1, choose the correct pair: (x0=0, x1=1), (x0=0, x1=2), (x0=1, x1=2), (x0=2, xl=4). b. Use the correct input to calculate x2. c. Calculate f(x2). d. According to the value of f(x2), should we replace x0 with x2, or replace x1 with x2? e. What is the next step of the algorithm? Will it continue the loop, or stop the loop? Why it will do so? Pseudocode for Bisection Method 1. Start 2. Define function f(x) 3. Input a. Lower and Upper guesses x0 and x1 b. tolerable error e 4. If f(x0)*f(x1) > 0 print "Incorrect initial guesses" goto 3 End If 5. Do x2 = (x0+x1)/2 If f(x0)*f(x2) < 0 x1 = x2 Else x0 = x2 End If while abs(f(x2)) > e 6. Print root as x2 7 Ston

Open with Numerical method 8. (Note: This question does not ask you to implement the algorithm. You do the calculation manually. This question tests your understanding of the algorithm.) Refer to the Pseudocode for Bisection Method. Suppose we want to use this algorithm to find a root of f(x)3(x+1)(x-3), and we input tolerable error e = 0.0001. a. Among the following pairs of initial guesses for x0 and x1, choose the correct pair: (x0=0, x1=1), (x0=0, x1=2), (x0=1, x1=2), (x0=2, xl=4). b. Use the correct input to calculate x2. c. Calculate f(x2). d. According to the value of f(x2), should we replace x0 with x2, or replace x1 with x2? e. What is the next step of the algorithm? Will it continue the loop, or stop the loop? Why it will do so? Pseudocode for Bisection Method 1. Start 2. Define function f(x) 3. Input a. Lower and Upper guesses x0 and x1 b. tolerable error e 4. If f(x0)*f(x1) > 0 print "Incorrect initial guesses" goto 3 End If 5. Do x2 = (x0+x1)/2 If f(x0)*f(x2) < 0 x1 = x2 Else x0 = x2 End If while abs(f(x2)) > e 6. Print root as x2 7 Ston

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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Open with Numerical method 8. (Note: This question does not ask you to implement the algorithm. You do the calculation manually. This question tests your understanding of the algorithm.) Refer to the Pseudocode for Bisection Method. Suppose we want to use this algorithm to find a root of f(x)=(x+1)(x-3), and we input tolerable error e a. Among the following pairs of initial guesses for x0 and x1, choose the correct pair: (x0=0, x1=1), (x0=0, x1=2), (x0=1, x1=2), (x0=2, x1=4). b. Use the correct input to calculate x2. c. Calculate f(x2). d. According to the value of f(x2), should we replace x0 with x2, or replace xl with x2? = 0.0001. %3D What is the next step of the algorithm? Will it continue the loop, or stop the loop? Why it will do so? е. Pseudocode for Bisection Method 1. Start 2. Define function f(x) 3. Input a. Lower and Upper guesses x0 and x1 b. tolerable error e 4. If f(x0)*f(x1) > 0 print "Incorrect initial guesses" goto 3 End If 5. Do x2 = (x0+x1)/2 If f(x0)*f(x2) < 0 x1 = x2 Else х0 %3D х2 End If while abs(f(x2)) > e 6. Print root as x2 7. Stop 2 I 3 + Page
Transcribed Image Text:Open with Numerical method 8. (Note: This question does not ask you to implement the algorithm. You do the calculation manually. This question tests your understanding of the algorithm.) Refer to the Pseudocode for Bisection Method. Suppose we want to use this algorithm to find a root of f(x)=(x+1)(x-3), and we input tolerable error e a. Among the following pairs of initial guesses for x0 and x1, choose the correct pair: (x0=0, x1=1), (x0=0, x1=2), (x0=1, x1=2), (x0=2, x1=4). b. Use the correct input to calculate x2. c. Calculate f(x2). d. According to the value of f(x2), should we replace x0 with x2, or replace xl with x2? = 0.0001. %3D What is the next step of the algorithm? Will it continue the loop, or stop the loop? Why it will do so? е. Pseudocode for Bisection Method 1. Start 2. Define function f(x) 3. Input a. Lower and Upper guesses x0 and x1 b. tolerable error e 4. If f(x0)*f(x1) > 0 print "Incorrect initial guesses" goto 3 End If 5. Do x2 = (x0+x1)/2 If f(x0)*f(x2) < 0 x1 = x2 Else х0 %3D х2 End If while abs(f(x2)) > e 6. Print root as x2 7. Stop 2 I 3 + Page
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