x = g(x) Iteration (Edexcel A-Level Mathematics): Quizzes

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x = g(x) Iteration
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What type of equations can fixed point iteration solve?

Simultaneous eqs where one is y=xy = x

What is the first step in the fixed point iterative method?

Choose start xx, find yy on curve

What must happen for the fixed point iterative method to find a root?

The process must converge

When does the change of sign method work?

When one side of equation equals 0

What property must a function have for change of sign to show a root exists in an interval?

Continuous in the interval

What do cobweb and staircase diagrams show in fixed point iteration?

How convergence takes place

To use fixed point iteration, x3+4x−3=0x^3 + 4x - 3 = 0 is rearranged into which form?

x=3−x34x = \frac{3-x^3}{4}

Using xn+1=3−xn34x_{n+1} = \frac{3-x_n^3}{4} with x1=0.5x_1 = 0.5, what is x2x_2 to 3 decimal places?

0.7190.719

How is 3x=x+33^x = x + 3 rearranged to form x=ln⁡(x+3)ln⁡3x = \frac{\ln(x+3)}{\ln 3}?

Taking logarithms of both sides

What are we solving simultaneously in fixed point iteration?

y=xy = x with y=g(x)y = g(x)

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