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Kalkulator Deret Taylor dan Maclaurin (Deret Pangkat)
Temukan deret Taylor/Maclaurin langkah demi langkah
Kalkulator akan menemukan ekspansi deret Taylor (atau deret pangkat) dari fungsi yang diberikan di sekitar titik yang ditentukan, dengan langkah-langkah ditampilkan. Anda dapat menentukan orde polinom Taylor. Jika Anda menginginkan polinom Maclaurin, cukup atur titik ke $$$0$$$.
Solution
Your input: calculate the Taylor (Maclaurin) series of $$$\frac{1}{x}$$$ up to $$$n=5$$$
A Maclaurin series is given by $$$f\left(x\right)=\sum\limits_{k=0}^{\infty}\frac{f^{(k)}\left(a\right)}{k!}x^k$$$
In our case, $$$f\left(x\right) \approx P\left(x\right) = \sum\limits_{k=0}^{n}\frac{f^{(k)}\left(a\right)}{k!}x^k=\sum\limits_{k=0}^{5}\frac{f^{(k)}\left(a\right)}{k!}x^k$$$
So, what we need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
$$$f^{(0)}\left(x\right)=f\left(x\right)=\frac{1}{x}$$$
Evaluate the function at the point: as can be seen, the function does not exist at the given point.
Answer: the Taylor (Maclaurin) series can't be found at the given point.