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

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

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taylor sqrt(1-2x^2)

taylor

1 - 2 x^{2}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 12}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 360}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 25200}{8 !} x^{8} + \dots

Refine

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

x \to 4 lim (x - 5)

\frac{d}{d x} (\frac{x ^{2} + 5}{e ^{x}})

\frac{s + 3}{s ^{2} + 4 s + 4}

\frac{1}{1 + 2 x ^{3}}

\int sec^{14} (x) tan (x) d x

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