What is taylor ln(3-x),2 ?

The answer to taylor ln(3-x),2 is -(x-2)-1/2 (x-2)^2-1/3 (x-2)^3-1/4 (x-2)^4-1/5 (x-2)^5+\ldots

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taylor ln(3-x),2

taylor

ln (3 - x), 2

- (x - 2) - \frac{1}{2} (x - 2)^{2} - \frac{1}{3} (x - 2)^{3} - \frac{1}{4} (x - 2)^{4} - \frac{1}{5} (x - 2)^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{- 1}{1 !} (x - 2) + \frac{- 1}{2 !} (x - 2)^{2} + \frac{- 2}{3 !} (x - 2)^{3} + \frac{- 6}{4 !} (x - 2)^{4} + \frac{- 24}{5 !} (x - 2)^{5} + \dots

Refine

= - (x - 2) - \frac{1}{2} (x - 2)^{2} - \frac{1}{3} (x - 2)^{3} - \frac{1}{4} (x - 2)^{4} - \frac{1}{5} (x - 2)^{5} + \dots

\int \frac{sec ^{2} ( x )}{x} d x

\int cos (nπ x) d x

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

x (x - 1)

y^{^{'}} = (x + 1)^{2}

What is taylor ln(3-x),2 ?
The answer to taylor ln(3-x),2 is -(x-2)-1/2 (x-2)^2-1/3 (x-2)^3-1/4 (x-2)^4-1/5 (x-2)^5+\ldots