What is taylor ln(x/2)2 ?

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

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taylor ln(x/2)2

taylor

ln (\frac{x}{2}) 2

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - 2 ln (2) + \frac{2}{1 !} (x - 1) + \frac{- 2}{2 !} (x - 1)^{2} + \frac{4}{3 !} (x - 1)^{3} + \frac{- 12}{4 !} (x - 1)^{4} + \dots

Refine

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

\int_{- 1}^{1} c (1 - x^{2}) d x

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

\frac{d y}{d x} = \frac{2 y}{x + 1}

x \to 1 lim (x + 4)

n = 1 \sum \infty \frac{n}{( 5 ^{n} )}

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