What is taylor ln(x+3) ?

The answer to taylor ln(x+3) 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(x+3)

taylor

ln (x + 3)

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

\frac{\partial}{\partial y} (- \frac{x}{x ^{2} + y ^{2}})

\frac{d}{d x} (sin (\frac{x ^{2} - 1}{x}))

\frac{\partial}{\partial x} (e^{2 x} cos (6 y))

\frac{d}{d x} (sin^{3} (cos (x)))

\frac{d ^{2} y}{d x ^{2}} = \frac{( 6 x ^{5} )}{5} - 3 x

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