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Alik [6]
3 years ago
14

Use Newton's method with initial approximation x1 = −2 to find x2, the second approximation to the root of the equation x3 + x +

7 = 0. (Round your answer to four decimal places.)
Mathematics
1 answer:
nevsk [136]3 years ago
5 0

Answer:

x_2 \approx -1.769

Step-by-step explanation:

Let f(x)=x^3+x+7

So f'(x)=3x^2+1

x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}

Let x_1=-2

We are going to find x_2

So we are evaluating -2-\frac{f(-2)}{f'(-2)}

First step find f(-2)

Second step find f'(-2)

Third step plug in those values and apply PEMDAS!

f(-2)=(-2)^3+(-2)+7=-8-2+7=-10+7=-3

f'(-2)=3(-2)^2+1=3(4)+1=12+1=13

So

x_2=-2-\frac{-3}{13} \\\\ x_2=\frac{-26+3}{13} \\\\ x_2=\frac{-23}{13} \\\\ x_2 \approx -1.769

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