What is taylor (1-x^2)^{(1/2)} ?

The answer to taylor (1-x^2)^{(1/2)} is 1-1/2 x^2-1/8 x^4-1/16 x^6-5/128 x^8+\ldots

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taylor (1-x^2)^{(1/2)}

taylor

(1 - x^{2})^{(\frac{1}{2})}

1 - \frac{1}{2} x^{2} - \frac{1}{8} x^{4} - \frac{1}{16} x^{6} - \frac{5}{128} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 1}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 3}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 45}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 1575}{8 !} x^{8} + \dots

Refine

= 1 - \frac{1}{2} x^{2} - \frac{1}{8} x^{4} - \frac{1}{16} x^{6} - \frac{5}{128} x^{8} + \dots

y = 3 x - 5

\frac{d}{d x} ((x^{5} - 2 x^{2})^{3} (4 x^{3} - 5)^{4})

\frac{\partial}{\partial y} (ln (2 x + y))

\frac{d}{d x} ((x^{2} + y^{2}) e^{x^{2} + y^{2}})

f (x) = \frac{6 x}{x ^{2} + 1}, at x = - 1

What is taylor (1-x^2)^{(1/2)} ?
The answer to taylor (1-x^2)^{(1/2)} is 1-1/2 x^2-1/8 x^4-1/16 x^6-5/128 x^8+\ldots