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1. The problem statement, all variables and given/known data

Use Newton’s method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.)

x^5+2=0, x_1=-1

2. Relevant equations

3. The attempt at a solution

x^{5}+2=0, x_{1}=-1

y'=5x^{4}

x_{(n+1)}=x_{n}-(x^{5}+2)/(5x^{4})

For n=1

x_{2}=-1-((-1)^{5}+2)/(5(-1)^{4})=-6/5=-1.2

For n=2

x_{3}=-1.2-((-1.2)^{5}+2)/(5(-1.2)^{4})= -1.2-0.4883/10.368=-1.2+0.047=-1.1530

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# Use Newton’s method with the specified initial approximation x1 to find x3.

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