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Simora [160]
3 years ago
8

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your ans

wers to four decimal places.) f(x) = cos x, x1 = 0.7
Mathematics
1 answer:
VikaD [51]3 years ago
4 0

Answer:

The two iterations of f(x) = 1.5598

Step-by-step explanation:

If we apply  Newton's iterations method, we get a new guess of a zero of a function, f(x), xₙ₊₁, using a previous guess of, xₙ.

xₙ₊₁ = xₙ - f(xₙ) / f'(xₙ)

Given;

f(xₙ) = cos x, then  f'(xₙ) = - sin x

cos x / - sin x = -cot x

substitute in "-cot x" into the equation

xₙ₊₁ = xₙ - (- cot x)

xₙ₊₁ = xₙ + cot x

x₁ = 0.7

first iteration

x₂ = 0.7 + cot (0.7)

x₂ =  0.7 + 1.18724

x₂ = 1.88724

 

second iteration

x₃ = 1.88724 + cot (1.88724)

x₃ = 1.88724 - 0.32744

x₃ = 1.5598

To four decimal places = 1.5598

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4.1<br> Determine between which two whole numbers lies square root of 20
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The square root of 20 is between 4 and 5.

<h3>Whole Numbers</h3>

They are the numbers represented by positive real numbers where the fractions and decimal numbers are not included.

For solving this question, you should list the whole numbers whose your square is less than 30. Your list must present the following numbers:

0 ⇒ 0²=0

1 ⇒ 1²=1

2 ⇒ 2²=4

3 ⇒3²=9

4 ⇒ 4²=16

5 ⇒ 5²=25

Note that 6²=36, it is greater than 30,because of this it is not in the previous list.

The question asks to determine between which two whole numbers lies the square root of 20. Therefore, from the previous list, it is possible to see that the value 20 is between 16 and 25. The square root of 16 and 25 is equal to 4 and 5, respectively.

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brainly.com/question/35767

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