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Suppose that we use the bisection algorithm to approximate r = √20 which the greatest zero of the function f(x)=x²-20. We begin by finding two numbers, say, a₁ = 4 and ₁ = 5 which bracket the zero. This is because f(a) <0 and f(b₁) > 0. Then we find m₁ = (a₁ + b₁)/2 = 4.5 and h₁ = (b₁-a₁)/2=0.5. We proceed with the bisection algorithm. Suppose that an, and b, bracket the zero. Then we compute m,= (a + b)/2 and hn = |bn-an/2. If f(mn) = 0 we stop because r = m, is the desired zero. If f(m₂) >0 then m,, becomes the new right endpoint, so we set an+1 = an and bn+1 = m₂. If f(mn) <0 then m, becomes the new left endpoint, so we set an+1 = mn and bn+1 = bn. Then m,, is an approximation to r with an error of h Complete the following table: n an bn hn min 14 5 0.5 4.5 2 3 4 5 Then is an approximation so far to r with an error of

Suppose that we use the bisection algorithm to approximate r = √20 which the greatest zero of the function f(x)=x²-20. We begin by finding two numbers, say, a₁ = 4 and ₁ = 5 which bracket the zero. This is because f(a) <0 and f(b₁) > 0. Then we find m₁ = (a₁ + b₁)/2 = 4.5 and h₁ = (b₁-a₁)/2=0.5. We proceed with the bisection algorithm. Suppose that an, and b, bracket the zero. Then we compute m,= (a + b)/2 and hn = |bn-an/2. If f(mn) = 0 we stop because r = m, is the desired zero. If f(m₂) >0 then m,, becomes the new right endpoint, so we set an+1 = an and bn+1 = m₂. If f(mn) <0 then m, becomes the new left endpoint, so we set an+1 = mn and bn+1 = bn. Then m,, is an approximation to r with an error of h Complete the following table: n an bn hn min 14 5 0.5 4.5 2 3 4 5 Then is an approximation so far to r with an error of

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose that we use the bisection algorithm to approximate r = √20 which the greatest zero of the function f(x)=x²-20. We begin by finding two numbers, say, a₁ = 4 and b₁ = 5 which bracket the zero. This is because f(ai) <0 and f(b₁) > 0. Then we find m₁ = -b₁)/2=4 and h₁ = (b₁-a1)/2=0.5. We proceed with the bisection algorithm. Suppose that an and bn bracket the zero. Then we compute m,= (an+b)/2 and hn = |bn-an/2. If f(mn) = 0 we stop because r = m, is the desired zero. If f(m₂) >0 then m,, becomes the new right endpoint, so we set an+1 = an and bn+1 = mn. If f(mn) < 0 then mn becomes the new left endpoint, so we set an+1 = mn and bn+1 = bn. Then mn is an approximation to r with an error of h Complete the following table: n an bn hn mn 14 5 0.5 4.5 2 3 4 15 Then is an approximation so far to r with an error of
Transcribed Image Text:Suppose that we use the bisection algorithm to approximate r = √20 which the greatest zero of the function f(x)=x²-20. We begin by finding two numbers, say, a₁ = 4 and b₁ = 5 which bracket the zero. This is because f(ai) <0 and f(b₁) > 0. Then we find m₁ = -b₁)/2=4 and h₁ = (b₁-a1)/2=0.5. We proceed with the bisection algorithm. Suppose that an and bn bracket the zero. Then we compute m,= (an+b)/2 and hn = |bn-an/2. If f(mn) = 0 we stop because r = m, is the desired zero. If f(m₂) >0 then m,, becomes the new right endpoint, so we set an+1 = an and bn+1 = mn. If f(mn) < 0 then mn becomes the new left endpoint, so we set an+1 = mn and bn+1 = bn. Then mn is an approximation to r with an error of h Complete the following table: n an bn hn mn 14 5 0.5 4.5 2 3 4 15 Then is an approximation so far to r with an error of
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