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a) Find the root of the equation f(x) = 2cosx-x² to 2 decimal places using the Newton-Raphson method. Using 1 as a first approximation.

a) Find the root of the equation f(x) = 2cosx-x² to 2 decimal places using the Newton-Raphson method. Using 1 as a first approximation.

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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Solve ( a) part only and plz use Blue pen to solve this i need clear and neat writing plz Also i don't need this answer if u upload this i will gave u thumb down
9:02 Step2 b) 1:40 Step3 c) Put formula Put n =1 f'(x) = given _||| n = 2 x3 4G 73% 04:29 - 2 sin x-2x x₁ = 1 x x2 = f(x) = xnh Anh f(1) = 2 cas1 - 01² f(x₂) xn- f'(x) Xn = -2xnsin 2 cas (xn)-x₂² -2 sin (x₂)-2xn (zn)-2x₁²_2cos(x) + x₂ ² - 2 sin (x₂)-2xn 2xn sin(x)- xn² - 2 cos(x) - 2 sin (²n) - 2x - 2 24 sin (24) - 24₁ ²-2 cos(x₂) - 2 sin (24)- 224 = - 2 sin (1) - 1-2 cos (1) - 2 Sin (1)-2 1.021 - 2x₂ sin (*₂) - 4-2 (as (x₂) √x 8 Xn+1 = x₂ =
Transcribed Image Text:9:02 Step2 b) 1:40 Step3 c) Put formula Put n =1 f'(x) = given _||| n = 2 x3 4G 73% 04:29 - 2 sin x-2x x₁ = 1 x x2 = f(x) = xnh Anh f(1) = 2 cas1 - 01² f(x₂) xn- f'(x) Xn = -2xnsin 2 cas (xn)-x₂² -2 sin (x₂)-2xn (zn)-2x₁²_2cos(x) + x₂ ² - 2 sin (x₂)-2xn 2xn sin(x)- xn² - 2 cos(x) - 2 sin (²n) - 2x - 2 24 sin (24) - 24₁ ²-2 cos(x₂) - 2 sin (24)- 224 = - 2 sin (1) - 1-2 cos (1) - 2 Sin (1)-2 1.021 - 2x₂ sin (*₂) - 4-2 (as (x₂) √x 8 Xn+1 = x₂ =
a) Find the root of the equation f(x) = 2cosx-x² to 2 decimal places using the Newton-Raphson method. Using 1 as a first approximation. b) Find the root of the equation f(x) = x − 2 + Inx that has a root near 1.5. Use the Newton-Raphson formula to obtain a better estimate to 4 d.p.
Transcribed Image Text:a) Find the root of the equation f(x) = 2cosx-x² to 2 decimal places using the Newton-Raphson method. Using 1 as a first approximation. b) Find the root of the equation f(x) = x − 2 + Inx that has a root near 1.5. Use the Newton-Raphson formula to obtain a better estimate to 4 d.p.
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