What is taylor ln(x+3)(1) ?

The answer to taylor ln(x+3)(1) 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)(1)

taylor

ln (x + 3) (1)

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

\frac{d}{d x} (\frac{6}{x + 4})

(15, 250), (20, 111)

\frac{8 - x}{5} + \frac{16 + x ^{2}}{3}

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

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