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BARSIC [14]
3 years ago
5

(04.02 MC)

Mathematics
1 answer:
Gennadij [26K]3 years ago
3 0
2447 it’s for sure it bc I did the math
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to lowest terms of 32:28 is 8/7 or 8:7

Step-by-step explanation:

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Use​ Newton's method to find an approximate solution of ln(x)=10-x. Start with x_0 =9 and find x_2 .
vova2212 [387]

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x₂ = 7.9156

Step-by-step explanation:

Given the function  ln(x)=10-x with initial value x₀ = 9, we are to find the second approximation value x₂ using the Newton's method. According to Newtons method xₙ₊₁ = xₙ -  f(xₙ)/f'(xₙ)

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x₁ = x₀ -  f(x₀)/f'(x₀)

x₁ = 9 -  1.1972/1.1111

x₁  = 9 - 1.0775

x₁  = 7.9225

x₂ = x₁ -  f(x₁)/f'(x₁)

x₂ = 7.9225 -  f(7.9225)/f'(7.9225)

f(7.9225) = ln7.9225 + 7.9225 -10

f(7.9225) = 2.0697 + 7.9225 -10

f(7.9225) = 0.0078

f'(7.9225) = 1/7.9225 + 1

f'(7.9225) = 0.1262+1

f'(7.9225) = 1.1262

x₂ = 7.9225 - 0.0078/1.1262

x₂ = 7.9225 - 0.006926

x₂ = 7.9156

<em>Hence the approximate value of x₂ is 7.9156</em>

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