What is taylor 9ln(5-8x^2) ?

The answer to taylor 9ln(5-8x^2) is 9ln(5)-72/5 x^2-288/25 x^4-1536/125 x^6-9216/625 x^8+\ldots

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taylor 9ln(5-8x^2)

taylor

9 ln (5 - 8 x^{2})

9 ln (5) - \frac{72}{5} x^{2} - \frac{288}{25} x^{4} - \frac{1536}{125} x^{6} - \frac{9216}{625} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 9 ln (5) + \frac{\frac{d}{d x} ( 9 ln ( 5 - 8 x ^{2} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 9 ln ( 5 - 8 x ^{2} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 9 ln ( 5 - 8 x ^{2} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 9 ln (5) + \frac{0}{1 !} x + \frac{- \frac{144}{5}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- \frac{6912}{25}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{221184}{25}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- \frac{74317824}{125}}{8 !} x^{8} + \dots

Refine

= 9 ln (5) - \frac{72}{5} x^{2} - \frac{288}{25} x^{4} - \frac{1536}{125} x^{6} - \frac{9216}{625} x^{8} + \dots

\frac{d y}{d t} = 3 + 2 y

y = x^{3} - 3 x - 4

\frac{d y}{d x} = \frac{2 x ( y - 1 )}{x ^{2} + 3}, y (1) = 9

\int \frac{x}{( x ^{2} + 1 ) ^{4}} d x

2 t \cdot cos (t)

What is taylor 9ln(5-8x^2) ?
The answer to taylor 9ln(5-8x^2) is 9ln(5)-72/5 x^2-288/25 x^4-1536/125 x^6-9216/625 x^8+\ldots