2secxtanx

2secxtanx

Input 2 sec(x) tan(x) Alternate form assuming x is real (4 sin(2 x) cos(x))/(cos(2 x) + 1)^2 Roots x = pi n, n element Z Series expansion at x=0 2 x + (5 x^3)/3 + (61 x^5)/60 + O(x^6) (Taylor series) Derivative d/dx(2 sec(x) tan(x)) = -(cos(2 x) – 3) sec^3(x) Indefinite integral integral 2 sec(x) tan(x) dx = 2 sec(x) + constant

2kr

2kr

Input interpretation 2 kr (Swedish kronor) Local currency conversion 20.15c (euro cents) (at current quoted rate) euro0.20 (euros) Additional currency conversions for 2 kr (Swedish kronor) USD | 23.80¢ (US cents) GBP | 17.80p (British pence) NOK | 1.97 kr (Norwegian kroner) DKK | 1.50 kr (Danish kroner) Countries of circulation Sweden Physical characteristics of a 2 kr coin diameter | 31 mm (millimeters) radius | 15.5 mm (millimeters) circumference | 97 mm (millimeters) area | 754.8 mm^2 (square millimeters)…

Read More Read More

214/4

214/4

Input 214/4 Exact result 107/2 Decimal form 53.5 Mixed fraction 53 1/2 Quotient and remainder 53×4 + 2 Prime factorization 2^(-1)×107 Continued fraction [53; 2] Egyptian fraction expansion 53 + 1/2

2sin2x

2sin2x

Input 2 sin(2 x) Roots x = (pi n)/2, n element Z Series expansion at x=0 4 x – (8 x^3)/3 + (8 x^5)/15 + O(x^6) (Taylor series) Derivative d/dx(2 sin(2 x)) = 4 cos(2 x) Indefinite integral integral 2 sin(2 x) dx = -cos(2 x) + constant Global maxima max{2 sin(2 x)} = 2 at x = pi n + pi/4 for integer n Definite integral over a half-period integral_0^(pi/2) 2 sin(2 x) dx = 2 Definite integral mean…

Read More Read More

214/7

214/7

Input 214/7 Exact result 214/7 (irreducible) Decimal approximation 30.57142857142857142857142857142857142857142857142857142857… Repeating decimal 30.571428^_ (period 6) Mixed fraction 30 4/7 Quotient and remainder 30×7 + 4 Prime factorization 2×7^(-1)×107 Continued fraction [30; 1, 1, 3] Egyptian fraction expansion 30 + 1/2 + 1/14 Occurrence in convergents (45 e)/4~~30, 31, 61/2, 153/5, 214/7, 367/12, 948/31, … (simple continued fraction convergent sequence)

2t 3t

2t 3t

Input 2 t (3 t) Result 6 t^2 Geometric figure parabola Root t = 0 Polynomial discriminant Delta = 0 Derivative d/dt(2 t (3 t)) = 12 t Indefinite integral integral 6 t^2 dt = 2 t^3 + constant Global minimum min{2 t (3 t)} = 0 at t = 0