What is taylor ln(1-3x) ?

The answer to taylor ln(1-3x) is -3x-9/2 x^2-9x^3-81/4 x^4-243/5 x^5+\ldots

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taylor ln(1-3x)

taylor

ln (1 - 3 x)

- 3 x - \frac{9}{2} x^{2} - 9 x^{3} - \frac{81}{4} x^{4} - \frac{243}{5} x^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( ln ( 1 - 3 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( 1 - 3 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( 1 - 3 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{- 3}{1 !} x + \frac{- 9}{2 !} x^{2} + \frac{- 54}{3 !} x^{3} + \frac{- 486}{4 !} x^{4} + \frac{- 5832}{5 !} x^{5} + \dots

Refine

= - 3 x - \frac{9}{2} x^{2} - 9 x^{3} - \frac{81}{4} x^{4} - \frac{243}{5} x^{5} + \dots

\frac{sec ( x )}{1 + sec ( x )}

\int_{4}^{6} f (x) d x

- \frac{1}{x + 1 ^{2}}

5 + 3 + x

f (x) = \frac{x - 1}{x ^{2} + 4}

What is taylor ln(1-3x) ?
The answer to taylor ln(1-3x) is -3x-9/2 x^2-9x^3-81/4 x^4-243/5 x^5+\ldots