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Solving Equations Numerically

Approximation
  • To find the root of a graph, find the point where the graph passes through the x-axis – look for a sign change.
  • Carry out a decimal search:
    • Substitute the values between where a sign change has occurred.
    • The closer to zero, the greater the accuracy.
Iteration
  • To solve the equation f(x) = 0, you can rearrange f(x) into a form x = …
  • This function represents a sequence that starts at x0, moving to xr
  • Substitute a value for x0 and put it into the function to get x1, and so on.
  • As you increase r, the value becomes more accurate.
  • Sometimes, iteration doesn’t work, these functions are called divergent, and you must rearrange the formula for x in another way.
  • For a successful iterative function, you need a convergent sequence.
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