## Y=x+1

Input |
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y = x + 1 |

Geometric figure |

line |

Alternate form |

-x + y – 1 = 0 |

Root |

x = -1 |

Derivative |

(d)/(dx)(x + 1) = 1 |

Input |
---|

y = x + 1 |

Geometric figure |

line |

Alternate form |

-x + y – 1 = 0 |

Root |

x = -1 |

Derivative |

(d)/(dx)(x + 1) = 1 |

Indefinite integral |
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integral sin^3(x) dx = 1/12 (cos(3 x) – 9 cos(x)) + constant |

Expanded form of the integral |

1/12 cos(3 x) – (3 cos(x))/4 + constant |

Series expansion of the integral at x=0 |

-2/3 + x^4/4 + O(x^6) (Taylor series) |

Definite integral over a half-period |

integral_0^pi sin^3(x) dx = 4/3~~1.33333 |

Definite integral mean square |

integral_0^(2 pi) (sin^6(x))/(2 pi) dx = 5/16 = 0.3125 |

Input interpretation |
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skype.com (domain) | topix.com (domain) |

Web hosting information |

| skype.com | topix.com name | Skype Technologies S.A. | Topix LLC location | Luxemburg, Luxembourg | Vancouver, Washington, United States coordinates | 49° 37′ 12″N, 6° 7′ 12″E | 45° 38′ 14″N, 122° 35′ 47″W |

Web statistics |

| skype.com | topix.com daily page views | ~~ 30 million hits/day (hits per day) (based on Alexa estimates, as of 2017-06-15) | ~~ 17 million hits/day (hits per day) (based on Alexa estimates, as of 2017-06-15) daily visitors | ~~ 9.2 million visits/day (visits per day) (based on Alexa estimates, as of 2017-06-15) | ~~ 1.4 million visits/day (visits per day) (based on Alexa estimates, as of 2017-06-15) site rank | ~~ 300th | ~~ 1540th domain online | 2003-04-23 (~~14 years ago) | 1995-03-02 (~~22 years ago) (based on Alexa estimates and assuming 3576810939 global internet users) |

Input |
---|

y = x^3 |

Alternate form |

y – x^3 = 0 |

Root |

x = 0 |

Derivative |

(d)/(dx)(x^3) = 3 x^2 |

Input interpretation |
---|

Roman semuncia |

Conversions to other units |

1 Roman semuncia | 0.5 Roman unciae | 0.0416667 Roman libras | 13.6437 grams | 0.0136437 kg (kilograms) | 0.481269 oz (ounces) |

Conversions from other units |

1 Roman uncia | 2 Roman semunciae 1 Roman libra | 24 Roman semunciae 1 g | 0.0732936 Roman semunciae 1 kg | 73.2936 Roman semunciae 1 oz | 2.07784 Roman semunciae |

Physical quantity |

mass |

Unit system |

Roman |

Input |
---|

y = abs(x) |

Alternate form assuming x and y are positive |

x = y |

Alternate form assuming x and y are real |

y = sqrt(x^2) |

Root |

x = 0 |

Derivative |

(d)/(dx)(abs(x)) = x/(abs(x)) |

Global minimum |

min{abs(x)} = 0 at x = 0 |

Input interpretation |
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series | sin(x) |

Series expansion at x=0 |

x – x^3/6 + x^5/120 + O(x^7) (Taylor series) |

Approximations about x=0 up to order 3 |

(order n approximation shown with n dots) |

Input |
---|

x^0 |

Result |

1 (for x!=0) |

Input interpretation |
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simplify | (7 + 1/y)/(x – y) |

Partial fraction expansion |

(-7 x – 1)/(x (y – x)) + 1/(x y) |

Input interpretation |
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topix.com (domain) | skype.com (domain) |

Web hosting information |

| topix.com | skype.com name | Topix LLC | Skype Technologies S.A. location | Vancouver, Washington, United States | Luxemburg, Luxembourg coordinates | 45° 38′ 14″N, 122° 35′ 47″W | 49° 37′ 12″N, 6° 7′ 12″E |

Web statistics |

| topix.com | skype.com daily page views | ~~ 17 million hits/day (hits per day) (based on Alexa estimates, as of 2017-06-15) | ~~ 30 million hits/day (hits per day) (based on Alexa estimates, as of 2017-06-15) daily visitors | ~~ 1.4 million visits/day (visits per day) (based on Alexa estimates, as of 2017-06-15) | ~~ 9.2 million visits/day (visits per day) (based on Alexa estimates, as of 2017-06-15) site rank | ~~ 1540th | ~~ 300th domain online | 1995-03-02 (~~22 years ago) | 2003-04-23 (~~14 years ago) (based on Alexa estimates and assuming 3576810939 global internet users) |