Root Finding

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IMPORTANT You will need to have a WolframAlpha Pro account to use Wolfram effectively.

Bisection Method

WolframAlpha can do the bisection method (just ask it bisection method x*sin(x) from 1 to 4) - however, it only gives you the final answer to the specified precision. Useful if you simply want to verify your answer. The solution gives you a diagram of convergence and the number of steps required to reach the set precision. There are several online calculators, including this one, which can be much more useful by giving intermediate steps. You can rapidly try out many functions to see how features like discontinuities, multiple equal roots and multiple packed roots behave.

Using either of these tools for the bisection method has its problems, though - you might not spot a discontinuity, for example, if you just type the equation in. Plotting the graph first (on Wolfram, Desmos, Matlab…) might help.

Newton-Raphson Method

Very similarly to the bisection method, Wolfram will do the Newton-Raphson method. The solution gives you a iteration diagram and the number of steps required to reach the set precision. But again, there are calculators (like this) that are more helpful: they also give each of the intermediate solutions before the final answer.

The disadvantage of the calculators over Wolfram is that many calculators require the function and its derivative to be inputted.