#### Solving Equations Numerically

__Approximation__

__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__

__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 x
_{0}, moving to x_{r} - Substitute a value for x
_{0}and put it into the function to get x_{1}, and so on. - As you increase r, the value becomes more accurate.
- Sometimes, iteration doesn’t work, these functions are calledÂ
*divergent*, and you must rearrange the formula for x in another way. - For a successful iterative function, you need a convergent sequence.