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## Homework Statement

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

## Homework Equations

## 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