Kiara Haas

2022-03-23

Maclaurin series for a function

Provided I have the function

$f\left(x\right)={(1+x)}^{\frac{1}{x}},$

and I want to calculate a 3rd order Maclaurin series, how can that be done without taking direct derivatives (as this seems hard..). I know that

${(1+x)}^{\frac{1}{x}}={e}^{\mathrm{ln}\frac{(1+x)}{x}},$

and the Maclaurin series for$e}^{x$ is easy to prove, so I think it's a good direction..

Provided I have the function

and I want to calculate a 3rd order Maclaurin series, how can that be done without taking direct derivatives (as this seems hard..). I know that

and the Maclaurin series for

aznluck4u72x4

Beginner2022-03-24Added 16 answers

Substitute -

so that

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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