Y=x+1

Y=x+1

Input
y = x + 1
Geometric figure
line
Alternate form
-x + y – 1 = 0
Root
x = -1
Derivative
(d)/(dx)(x + 1) = 1
Integral of sin^3

Integral of sin^3

Indefinite integral
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
Skype topix

Skype topix

Input interpretation
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)
Secuencia

Secuencia

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
Y=absolute value of x

Y=absolute value of x

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
Taylor series for sinx

Taylor series for sinx

Input interpretation
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)
Topix skype

Topix skype

Input interpretation
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)