Input interpretation Number Theory > Arithmetic > Fractions | Number Theory > Arithmetic > Fractions

Input abs(x) Alternate form assuming x>0 x Alternate form assuming x is real sqrt(x^2) Root x = 0 Derivative d/dx(abs(x)) = x/abs(x) (assuming a function from reals to reals) Indefinite integral assuming all variables are real integral abs(x) dx = 1/2 x^2 sgn(x) + constant Global minimum min{abs(x)} = 0 …

Input interpretation complete the square | 28 + 10 x + x^2 Result (x + 5)^2 + 3 Geometric figure parabola Polynomial discriminant Delta = -12 Derivative d/dx((x + 5)^2 + 3) = 2 (x + 5) Indefinite integral integral (3 + (5 + x)^2) dx = x^3/3 + 5 …

Input interpretation arithmetic progression Alternate name arithmetic sequence Definition An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0 + kd}_(k = 0)^(n – 1) such that the differences between successive terms is a constant d. An arithmetic progression can be generated in the …

Input sqrt(12) Result 2 sqrt(3) Decimal approximation 3.464101615137754587054892683011744733885610507620761256111… Continued fraction [3; 2, 6^_]