When working with equations, use Plot to visualize them. Further, a simple but powerful method to solve them is:

Here's a short example adapted from

Use TraditionalForm to put an expression in traditional math format:

sin(x) = x – 1

With Plot we visualize the two terms of the equation as separate functions and their intersection, indicating where they zero each other out near x = 2. Giving Plot the two terms in a List says 'Plot y = sin(x) and y = x - 1 together.' The first function is blue, the second, yellow.

Since we have flushed out a root, we can use FindRoot to precisely locate it, supplying FindRoot with a guess that it's near x = 2. Giving FindRoot a single coordinate causes it to use the Newton-Raphson method, while giving it two coordinates causes it to use a secant method.

{x->1.93456}

Always verify the solution.

True

- Plot the equation
- Find an x-value close to a root
- Use that value as the initial guess
*x*in FindRoot, which uses numerical methods_{0}

Here's a short example adapted from

*The Student's Introduction to Mathematica*. What is instructive is they Plot the two components of the equation separately. Analyzing and plotting each term separately is essential to understanding the equation as a whole.Use TraditionalForm to put an expression in traditional math format:

**Sin@x==x-1//TraditionalForm**sin(x) = x – 1

With Plot we visualize the two terms of the equation as separate functions and their intersection, indicating where they zero each other out near x = 2. Giving Plot the two terms in a List says 'Plot y = sin(x) and y = x - 1 together.' The first function is blue, the second, yellow.

**Plot[{Sin@x, x - 1}, {x, -6, 6}]**

**soln1=FindRoot[Sin@x==x-1,{x,2}]**{x->1.93456}

Always verify the solution.

**Sin@x==x-1/.soln1**True

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