Indefinite integral integral sin(X) 3 dX = -3 cos(X) + constant Alternate form of the integral -3/2 e^(-i X) – (3 e^(i X))/2 + constant Series expansion of the integral at X=0 -3 + (3 X^2)/2 – X^4/8 + O(X^6) (Taylor series) Definite integral over a half-period integral_0^pi 3 sin(X) dX = 6 Definite integral […]
Input interpretation plane curve | Cartesian equation y = 1 + 3 x | x-intercept Result -1/3~~-0.333333 Geometric figure line Properties of line x-intercept | -1/3~~-0.333333 y-intercept | 1 slope | 3
Input interpretation irreducible fraction Definition An irreducible fraction is a fraction p/q for which GCD(p, q) = 1, i.e., p and q are relatively prime. For example, in the complex plane, (4 + 7i)/(2 + i) = 3 + 2i is reducible, while (5 + 5i)/(7 + i) = 4/5 + 3i/5 is not. The […]
Input interpretation is 128 a perfect square number? Result 128 is not a perfect square number Nearest perfect square numbers 121 | 144 Formula for the nth perfect square number P(4,n) = n^2 (for positive integers n) Generating function for the perfect square numbers sum_(n=1)^infinity P(4,n) x^n = (-x^2 – x)/(x – 1)^3
Input interpretation is 288 a perfect square number? Result 288 is not a perfect square number Nearest perfect square numbers 256 | 289 Formula for the nth perfect square number P(4,n) = n^2 (for positive integers n) Generating function for the perfect square numbers sum_(n=1)^infinity P(4,n) x^n = (-x^2 – x)/(x – 1)^3
Input interpretation is 289 a perfect square number? Result 289 is a perfect square number Formula for the nth perfect square number P(4,n) = n^2 (for positive integers n) Generating function for the perfect square numbers sum_(n=1)^infinity P(4,n) x^n = (-x^2 – x)/(x – 1)^3 Position in sequence 289 is the 17th perfect square number
Input interpretation is 3.67 a rational number? Result 3.67 is a rational number Rational representation 367/100 Mixed fraction 3 67/100 Quotient and remainder 3×100 + 67 Egyptian fraction expansion 3 + 1/2 + 1/6 + 1/300
Input interpretation is 324 a perfect square number? Result 324 is a perfect square number Formula for the nth perfect square number P(4,n) = n^2 (for positive integers n) Generating function for the perfect square numbers sum_(n=1)^infinity P(4,n) x^n = (-x^2 – x)/(x – 1)^3 Position in sequence 324 is the 18th perfect square number
Input interpretation kg/(m s^2) (kilogram per meter per second squared) Conversion to other unit 1 kg/(m s^2) | 1000 g/(m s^2) (grams per meter per second squared) Conversion from other unit 1 g/(m s^2) | 0.001 kg/(m s^2) Unit system Système International d’Unités (SI) Basic unit dimensions [mass] [length]^(-1) [time]^(-2)