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Show that if h>0, applying Newton's method to the following function leads to x₁ = -h if x = h and to x₁ =h if x = -h. Draw a picture that shows what is going on. √x, x20 √√√-x, x<0 f(x)= First, identify the approximation formula for Newton's method. Choose the correct answer below. A. Xn+1=Xn- OB. Xn+1=Xn- f(xn) OD. Xn+1=Xn+ 5, if f' (xn) #0 f (xn) f(xn) OC. Xn+1=Xn-f(xn) -f(xn) -, if f(xn) #0 f(xn) 'f'(xn)' , if f'(xn) *0 Find the derivative of √x. d & √x =

Show that if h>0, applying Newton's method to the following function leads to x₁ = -h if x = h and to x₁ =h if x = -h. Draw a picture that shows what is going on. √x, x20 √√√-x, x<0 f(x)= First, identify the approximation formula for Newton's method. Choose the correct answer below. A. Xn+1=Xn- OB. Xn+1=Xn- f(xn) OD. Xn+1=Xn+ 5, if f' (xn) #0 f (xn) f(xn) OC. Xn+1=Xn-f(xn) -f(xn) -, if f(xn) #0 f(xn) 'f'(xn)' , if f'(xn) *0 Find the derivative of √x. d & √x =

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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Show that if h>0, applying Newton's method to the following function leads to x₁ = −h if x = h and to x₁ = h if x = - h. Draw a picture that shows what is going on. √x, x≥0 -x, x<0 f(x) = First, identify the approximation formula for Newton's method. Choose the correct answer below. Xn+1=Xn 'f'(xn) if f'(xn) #0 ' f (xn) B. Xn+1=Xn f(xn) Xn+1 = xn− f'(Xn) − f (xn) - D. Xn+1=Xn+ ,iff(xn) #0 f(xn) 'f'(xn) ' Find the derivative of √√x. d dx = ‚ if f' (xn) #0
Transcribed Image Text:Show that if h>0, applying Newton's method to the following function leads to x₁ = −h if x = h and to x₁ = h if x = - h. Draw a picture that shows what is going on. √x, x≥0 -x, x<0 f(x) = First, identify the approximation formula for Newton's method. Choose the correct answer below. Xn+1=Xn 'f'(xn) if f'(xn) #0 ' f (xn) B. Xn+1=Xn f(xn) Xn+1 = xn− f'(Xn) − f (xn) - D. Xn+1=Xn+ ,iff(xn) #0 f(xn) 'f'(xn) ' Find the derivative of √√x. d dx = ‚ if f' (xn) #0
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