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

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

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taylor ln(x+3),-1

taylor

ln (x + 3), - 1

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

\frac{d}{d t} ((t^{4} - 2 t)^{2} - 5)

\int_{0}^{9} 81 - x^{2} d x

x^{y} = y^{x}

\int \frac{x ^{3}}{e ^{x^{4}}} d x

\frac{\partial}{\partial z} (3 y)

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