What is taylor ln(7-3x),2 ?

The answer to taylor ln(7-3x),2 is -3(x-2)-9/2 (x-2)^2-9(x-2)^3-81/4 (x-2)^4-243/5 (x-2)^5+\ldots

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taylor ln(7-3x),2

taylor

ln (7 - 3 x), 2

- 3 (x - 2) - \frac{9}{2} (x - 2)^{2} - 9 (x - 2)^{3} - \frac{81}{4} (x - 2)^{4} - \frac{243}{5} (x - 2)^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( ln ( 7 - 3 x ) ) ( 2 )}{1 !} (x - 2) + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( 7 - 3 x ) ) ( 2 )}{2 !} (x - 2)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( 7 - 3 x ) ) ( 2 )}{3 !} (x - 2)^{3} + \dots

Evaluate Derivatives

= 0 + \frac{- 3}{1 !} (x - 2) + \frac{- 9}{2 !} (x - 2)^{2} + \frac{- 54}{3 !} (x - 2)^{3} + \frac{- 486}{4 !} (x - 2)^{4} + \frac{- 5832}{5 !} (x - 2)^{5} + \dots

Refine

= - 3 (x - 2) - \frac{9}{2} (x - 2)^{2} - 9 (x - 2)^{3} - \frac{81}{4} (x - 2)^{4} - \frac{243}{5} (x - 2)^{5} + \dots

\frac{d}{d x} (\frac{7}{4 - 3 x})

\frac{d}{d x} (cos^{2} (a - x))

f (x) = \frac{x + x ^{3}}{x}

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

x \to 4 lim (\frac{5}{x - 3})

What is taylor ln(7-3x),2 ?
The answer to taylor ln(7-3x),2 is -3(x-2)-9/2 (x-2)^2-9(x-2)^3-81/4 (x-2)^4-243/5 (x-2)^5+\ldots