What is taylor sqrt(1-3x^2) ?

The answer to taylor sqrt(1-3x^2) is 1-3/2 x^2-9/8 x^4-27/16 x^6-405/128 x^8+\ldots

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taylor sqrt(1-3x^2)

taylor

1 - 3 x^{2}

1 - \frac{3}{2} x^{2} - \frac{9}{8} x^{4} - \frac{27}{16} x^{6} - \frac{405}{128} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 3}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 27}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 1215}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 127575}{8 !} x^{8} + \dots

Refine

= 1 - \frac{3}{2} x^{2} - \frac{9}{8} x^{4} - \frac{27}{16} x^{6} - \frac{405}{128} x^{8} + \dots

f^{^{'}} (x) = f (x) (1 - f (x))

\int \frac{( 7 sin ( x ) + 4 sec ( x ) )}{tan ( x )} d x

f (x) = 200 + \frac{7}{x} + \frac{x ^{2}}{7}

y^{^{'}} = x (9 - y)

n = 1 \sum \infty \frac{1}{n + 9}

What is taylor sqrt(1-3x^2) ?
The answer to taylor sqrt(1-3x^2) is 1-3/2 x^2-9/8 x^4-27/16 x^6-405/128 x^8+\ldots