What is taylor ln(x),6 ?

The answer to taylor ln(x),6 is ln(6)+1/6 (x-6)-1/72 (x-6)^2+1/648 (x-6)^3-1/5184 (x-6)^4+\ldots

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taylor ln(x),6

taylor

ln (x), 6

ln (6) + \frac{1}{6} (x - 6) - \frac{1}{72} (x - 6)^{2} + \frac{1}{648} (x - 6)^{3} - \frac{1}{5184} (x - 6)^{4} + \dots

Solution steps

Apply the Taylor Formula

= ln (6) + \frac{\frac{d}{d x} ( ln ( x ) ) ( 6 )}{1 !} (x - 6) + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( x ) ) ( 6 )}{2 !} (x - 6)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( x ) ) ( 6 )}{3 !} (x - 6)^{3} + \dots

Evaluate Derivatives

= ln (6) + \frac{\frac{1}{6}}{1 !} (x - 6) + \frac{- \frac{1}{36}}{2 !} (x - 6)^{2} + \frac{\frac{1}{108}}{3 !} (x - 6)^{3} + \frac{- \frac{1}{216}}{4 !} (x - 6)^{4} + \dots

Refine

= ln (6) + \frac{1}{6} (x - 6) - \frac{1}{72} (x - 6)^{2} + \frac{1}{648} (x - 6)^{3} - \frac{1}{5184} (x - 6)^{4} + \dots

\frac{d}{d x} (8 + 3 sin (x))

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

n = 1 \sum \infty \frac{1}{2 ^{n} n !}

x y^{^{'}} + y = 37 x

What is taylor ln(x),6 ?
The answer to taylor ln(x),6 is ln(6)+1/6 (x-6)-1/72 (x-6)^2+1/648 (x-6)^3-1/5184 (x-6)^4+\ldots