In my calculus textbook, it shows that a function's solution can be approximated using an approximated function tangent to the original function based on an approximated solution, where the equation to find the approximated is L(x) = f(X0) + f'(X0)*(X-X0), where when rearranged, gives x = Xo - (f(X0)/f'(X0)) it doesn't give any reasoning as to why this is the equation. I do understand that the f(X0)/f'(X0) does in some way represent the margin of error of X0, and would (asymptotically) approach this margin of error, but never fully reach it (at least in the cases of the example equations given by the textbook). However, I would like to know how it works and how this equation was derived.(adsbygoogle = window.adsbygoogle || []).push({});

Any help would be appreciated, thanks.

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# I Newton's method for approximating solutions of functions

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