What is taylor ln(x),3 ?

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

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taylor ln(x),3

taylor

ln (x), 3

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

in v erse l a pl a ce \frac{1}{( s + 2 ) ^{2}}

\frac{d y}{d x} = y x

\int_{0}^{3} 2 π (x) (3 x - x^{2}) d x

d er i v a t i v e \frac{2}{3} (4 y^{2} + \frac{1}{2})^{\frac{3}{2}}

\frac{d}{d t} (2 t)

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