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Select the correct answer. Consider these equations: f(x)=[tex]x^{3}[/tex]+3 g(x)=[tex]x^{2}[/tex]+2 Approximate the solution to the equation f(x) = g(x) using three iterations of successive approximation. Use this graph as a starting point.

Select the correct answer Consider these equations fxtexx3tex3 gxtexx2tex2 Approximate the solution to the equation fx gx using three iterations of successive a class=

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osikbro

Answer:

A

Step-by-step explanation:

The solution to these two graphs will be when they are equal. Therefore:

[tex]x^3+3=x^2+2 \\\\x^3-x^2+1=0 \\\\x\approx -0.755\approx -\dfrac{13}{16}[/tex]

Hope this helps!

wegnerkolmp2741o

Answer:

-13/16

Step-by-step explanation:

f(x)=x^3+3

g(x)=x^2+2

We know the solution is around -1

x^3+3 = x^2 +2

Subtract x^2+2 from each side

x^3 -x^2 -1 = f(x)

We need to find the derivative

3x^2 -2x = f'(x)

Newtons method of successive approximation states

xn+1 = xn -f(xn) / f'(xn)

Function

x3−x2+1

Derivative

x⋅(3⋅x−2)

x

-0.75488

Iterations

Step x F(x) |x(i) - x(i-1)|

x1 -0.8      -0.152000 0.152000

x2 -0.75682 -0.006259 0.006259

x3 -0.75488 -0.000012 0.000012

The approximate answer is -0.75488

The closest answer given is -13/16

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