# Sqrt(1-x^2)

Input |
---|

sqrt(1 – x^2) |

Alternate form |

sqrt(1 – x) sqrt(x + 1) |

Series expansion at x=-1 |

sqrt(2) sqrt(x + 1) – (x + 1)^(3/2)/(2 sqrt(2)) – (x + 1)^(5/2)/(16 sqrt(2)) + O((x + 1)^(7/2)) (Puiseux series) |

Series expansion at x=0 |

1 – x^2/2 – x^4/8 + O(x^5) (Taylor series) |

Series expansion at x=1 |

i sqrt(2) sqrt(x – 1) + (i (x – 1)^(3/2))/(2 sqrt(2)) – (i (x – 1)^(5/2))/(16 sqrt(2)) + O((x – 1)^(7/2)) (Puiseux series) |

Series expansion at x=∞ |

i x – i/(2 x) – i/(8 x^3) + O((1/x)^4) (Laurent series) |

Derivative |

d/dx(sqrt(1 – x^2)) = -x/sqrt(1 – x^2) |

Indefinite integral |

integral sqrt(1 – x^2) dx = 1/2 (sqrt(1 – x^2) x + sin^(-1)(x)) + constant |

Global maximum |

max{sqrt(1 – x^2)} = 1 at x = 0 |

Definite integral |

integral_(-1)^1 sqrt(1 – x^2) dx = pi/2~~1.5708 |