Question
Asked Oct 2, 2019
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Use the Newton-Raphson method to find an approximate solution of the equation

e-7x = x

in the interval [0, 1]. Use the method until successive approximations obtained by a calculator are identical.

x ≈ 
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Expert Answer

Step 1

The function

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f(x)e-x Differentiate with respect to x -7x f(x)-7e-1 Use newton's method f(x,) -7x = X _]e1%n -1 -x,-e -7e1-1 -x 7x,e -7xm -7x,e -Te e -7x- -7e1-1 -7x = e

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Step 2

Compute first iteration.

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Let x0 -7x6-1 -7e101 -7(x0) --7(0)- -7e7(0) -1 1 =0.125

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Step 3

Compute second i...

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Let x 0.125 xz =e)-7x, -1 -7e-1 = e 7(0.125)7(0.125)-1 -Te(0.125)_1 0.199491954235 Compute third iteration Let x 0.199491954235 x, =e)-7x, -1 -7e-1 -7(0.1994 91954235)7(0.199491954235)-1 -Je7(0.199491954235)_1 = e =0.217053366926

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