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I am trying to write a report on taylor series for numerical analysis I need to...

I am trying to write a report on taylor series for numerical analysis I need to know what is it used for in most cases applying numerical techniques and what are the benefits of taylor series and if theres any disadvantages at all?

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The biggest advantage of this method is simply how easily you can calculate even the most complex functions. This is especially important for the computers which can only compute using basic arithmetic.

The disadvantage is how long it will take to compute.

There are also applications in physics if a system under a conservative force is at a stable equilibrium point x0 then there are no net forces And the energy function is concave upwards in terms of Taylor series The energy function U in the form of... U(X)=U0+k(x-x0)^2+k(x-x0) ^3

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