What is taylor ln(3-x) ?

The answer to taylor ln(3-x) is ln(3)-1/3 x-1/18 x^2-1/81 x^3-1/324 x^4+\ldots

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taylor ln(3-x)

taylor

ln (3 - x)

ln (3) - \frac{1}{3} x - \frac{1}{18} x^{2} - \frac{1}{81} x^{3} - \frac{1}{324} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= ln (3) + \frac{- \frac{1}{3}}{1 !} x + \frac{- \frac{1}{9}}{2 !} x^{2} + \frac{- \frac{2}{27}}{3 !} x^{3} + \frac{- \frac{2}{27}}{4 !} x^{4} + \dots

Refine

= ln (3) - \frac{1}{3} x - \frac{1}{18} x^{2} - \frac{1}{81} x^{3} - \frac{1}{324} x^{4} + \dots

\int \frac{1}{1 + 28 x} d x

\frac{d}{d x} (tan (x) \cdot 107.55)

\frac{d}{d x} (\frac{x ^{10}}{20} + \frac{1}{16 x ^{8}})

\frac{\partial}{\partial x} (e^{\frac{y}{x}})

What is taylor ln(3-x) ?
The answer to taylor ln(3-x) is ln(3)-1/3 x-1/18 x^2-1/81 x^3-1/324 x^4+\ldots