What is taylor ln(x+2) ?

The answer to taylor ln(x+2) is ln(2)+1/2 x-1/8 x^2+1/24 x^3-1/64 x^4+\ldots

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taylor ln(x+2)

taylor

ln (x + 2)

ln (2) + \frac{1}{2} x - \frac{1}{8} x^{2} + \frac{1}{24} x^{3} - \frac{1}{64} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= ln (2) + \frac{\frac{1}{2}}{1 !} x + \frac{- \frac{1}{4}}{2 !} x^{2} + \frac{\frac{1}{4}}{3 !} x^{3} + \frac{- \frac{3}{8}}{4 !} x^{4} + \dots

Refine

= ln (2) + \frac{1}{2} x - \frac{1}{8} x^{2} + \frac{1}{24} x^{3} - \frac{1}{64} x^{4} + \dots

\int x^{3} 5^{- x} d x

\int (x^{2} + 2 x - 1) cos (3 x) d x

\int_{0}^{1} e^{\frac{2 x}{3}} d x

\frac{d y}{d x} = \frac{( x + sin ( x ) )}{3 y ^{2}}

x^{3} - 2 x^{2} + 4 x + 3

What is taylor ln(x+2) ?
The answer to taylor ln(x+2) is ln(2)+1/2 x-1/8 x^2+1/24 x^3-1/64 x^4+\ldots