http://www.WolframAlpha.com:  calcolatrice Numerica / Simbolica [utile, tra l'altro, per semplificare espressioni ottenute con R]; prova a svolgere i "calcoli" seguenti;  molti altri esempi li hai cliccando "Examples", poi "Mathematics" e, quindi, se vuoi, cliccando "Elementary Mathematics", ..., "Famous Math Problems" (altri esempi significativi li trovi in "Statistics & Data Analysis", "Physics", "Chemistry", "Money & Finance", "Computational Sciences", "Units & Measures" -  per copiare i risultati basta cliccare, nella applicazione, su di essi e copiarli dalla nuova finestra in cui appaiono;  poi se si vuole si torna indietro, alla finestra con in input il termine originale - ovviamente, puoi aprire WolframAlpha in più finestre;  altre considerazioni ed esempi li puoi trovare in mathworld.wolfram.com;  esempi riferiti ai vari temi matematici / agli OM).  Se si sta operando su un computer che non è il proprio, WolframAlpha è uno strumento comodissimo per fare elaborazioni senza dover installare nulla.  SPOT

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1/6+5/9
0.123...
0.12323...
sqrt(1234567890)
cuberoot(1234567890)
3.5 days -> hours
sort (3,5,6,1,9,4)
sort ("maria", "luigi", "dario", "piera", "rosa", "alfonso")
pie chart (1, 2, 3)
BarChart (2, 7, 4)
histogram{156,168,162,150,167,157,170,157,159,164,157,165,163,165,160,163,162,155}
statistics{156,168,162,150,167,157,170,157,159,164,157,165,163,165,160,163,162,155}
triangle vertices (1,1), (2,4), (3,3)
triangle sides  1,4,4
 (poi clicca "0.324166 radians", ...)
pi
pi to 1000 digits
 (numeri le cui approssimazioni sono:)
4.7082
6.038504
2.598076211353
4.71 through pi and e
Is 5^(1/3) a rational number?
Is pi^sqrt(2) a rational number?
factor 70560
primes between 8700 and 8900
9^9^9
1+2+3+...+10
1+0.5^1+0.5^2+0.5^3+...
1+0.5+0.5^2+0.5^3+...
sum 0.5^n, n=0 to 20
sum 0.5^n, n=0 to oo
factorial(100)
mathworld subject terminology
statistics
statistics maths
descriptive statistics
mathworld subject probability
mathworld subject limit theorems
calculus maths
geometry maths
geometry
 (anche cliccando poi su Refferring to Maths Def)
geometric transformations
 (cliccando sia "general topic" che "a class of...")
mathworld subject algebraic properties
mathworld subject general algebra
polynomial
polynomials
vectors
functions definition
periodic function
derivative definition
integral definition
area definition
curve
surface
median, mean
complex numbers
power series
matrix
 (cliccando sia "general topic" che "referring to a...")
subject general projective geometry
mathworld subject continuous distributions
mathworld subject discrete distributions
mathworld subject miscellaneous transformations
mathworld subject functions
mathworld subject game theory
mathworld subject matrix types
famous mathematical games
mathworld subject rounding
mathworld subject error analysis
mathworld subject proofs
mathworld subject general logic
mathworld subject notation
solved mathematics problems
mathematical paradoxes
sphere, surface area=1
polygon area
 (cliccando "referring to a...")
rotate 30 degrees
reflect across y=2x
vertical shear 30 degrees
cardioid
annulus, inner radius=2, outer radius=5
What is the radius of a cone with volume v and height 2
219 to base 2
11011011 from base 2 to base 10
16.2 to base 2
prime between 2000000 and  2000100
prime closest to 200000000000
basic definition of prime number
gcd 2261, 74613
lcm 2261, 74613
1563 to roman
historical numerals
binomial(7,n) where n = 0,1,2,3,4,5,6,7
binomial(2*n,n)*(1/2^n)*(1/2^n) where n = 1,2,3,4,5,6,7,8,9,10
plot binomial(2*n,n)*(1/2^n)*(1/2^n) where n = 1,2,3,4,5,6,7,8,9,10
solve x^2-x=3.2
x^2-x=3.2
y=x^2
plot y = x^3-x, x=15
plot y^2+x^2-x=1, y=x^2, y^2=x, y=0, x=0
y = Piecewise[ { {x^2, 1>x>=0}, {x, 0>x>-1}, {-1, -1>x } } ]
range y = x*x*x - 3*x*x + 1, -5 < x < 10
inverse of F(x) = x^2+x
 (si ottiene la relazione inversa, non necessariamente una funzione; vedi anche qui)
number line x^2>=1, 0<=x<2
sin(x) = sqrt(3)/2, sin(5*x)
square(center=(0,0),side=2), segment (0,0) (sin(60*PI/180),cos(60*PI/180)), circle x^2+y^2=1
x+y=1 & x-y=1
solve x^7-x^6-x^5-x+1+sin(x)=0 for x
 (attenzione: non è detto che si ottengano tutte le soluzioni:)
plot y=x^7-x^6-x^5-x+1+sin(x) for -2 <= x <= 2, -3 <= y <= 3
 (se specifico l'intervallo posso ottenere [tutte] le soluzioni in esso)
solve x^7-x^6-x^5-x+1+sin(x)=0 for x, -10 <= x <= 10
plot y = sqrt(25+4*x-4*x^2)), -3 <= x <= 4
real plot y = sqrt(25+4*x-4*x^2)), -3 <= x <= 4
plot y = sin(x) and y = sin(x/180*PI),  0 <= x <= 2*PI
(3*x^4-x^3) / (x^2-x+2)
 [ottengo 3*x^2 + 2*x - 4 + (8x-8)/(x^2-x+2): 3*x^2+2*x-4 e resto 8x-8]
quotient and remainder of  (3*x^4-x^3) / (x^2-x+2)
 ( click [Show details] )
gcd(x^2–8x+15, x^2–10x+21)
lcm(x^2–8x+15, x^2–10x+21)
line (1,2) (2,1)
point point distance
point line distance
plot x^2+y^2<1 and y>x
circle (0,0), (1,0), (0,1)
parametric plot (3*sin(t), 2*cos(t))
pentagon
a*x^5-2*a*x^3+a*x
(x^3+1)/(x+1)
sin(x+y)
x^3 - 4*x^2 + 6*x - 24 = 0
solve x^2+y^2+z^2-1 = 0 for x
solve 7*x^4 + sqrt(3)*x^3-  x^2 + 2*x + 2/3 = 0 for x real
solve 7*x^4 + sqrt(3)*x^3-  x^2 + 2*x + 2/3 = 0 for x
factor
factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48
stationary points of (x^5+x^9-x-1)^3
inflection points of (x^5+x^9-x-1)^3
asymptotes (2x^3 + 4x^2 - 9)/(3 - x^2)
cusps of |x-2|^(1/2)-|x+2|^(1/3)
tangent to x*e^-x^2 at x=1/3
tangent to 2*x^2 + 2*y^2 - 8*y + 1 = 0 passing through (2,3)
2x^2 - 3xy + 4y^2 + 6x - 3y - 4 = 0
5, 14, 23, 32, 41, ...
f(n+1)=f(n)*2, f(0)=1
recursion
sequences
sum 1/n^2, n=1 to oo
sum x^n, n=0 to +oo
NOT(P AND (Q OR P))
(complement S) intersect (A union B)
d/dx cos(x)^2*x
d/dx cos(x)^2*x at x=pi/4
derivative of x^4*sin(x)
d(f(x)*g(x))/dx
d/dx piecewise[ { {x^2, x>=0}, {0, x<0} } ]
lim (sin(x)-x)/x^3 as x->0
lim (x-sin(x)/2-log(1+x)/2) / ( x*(1-cos(x) ) )  as x->0
limit
d^3/dx^3 (x^2+x^3+sin(2*x))
(d^1/dx^1) sin(x), (d^2/dx^2) sin(x), (d^3/dx^3) sin(x), (d^4/dx^4) sin(x)
d/dx d/dy x^3*y^4
maximize x(1-x)e^x
integrate sin x dx from x=0 to pi
integrate sin(cos x) from x=0 to 1
integrate piecewise[ { {x^2, x <= 2}, {x, 2 < x} } ] x = -1..3
plot piecewise[{  {x, x <= 1}, { (x-1)*2 , 1 < x <= 1.5}, { (2-x)*2 , 1.5 < x} }], x = 0..2
integrate piecewise[{  {x, x <= 1}, { (x-1)*2 , 1 < x <= 1.5}, { (2-x)*2 , 1.5 < x} }], x = 0..2
integrate sin
integrate x^3+1/x dx
 (ma è meglio mettere solo x^3+1/x ... per interpretare l'uscita fornita)
integrate sin(x)/x dx
 (l'integrale non è una funzione elementare)
int sin(x)/x dx, x=0..infinity
area between y=|x| and y=x^2-10
arc length of y=sqrt(1-x^2) from x=-1 to x=1
d/dx (integrate exp(-t^2) from t=2*x to 3*x)
taylor series sin(x) at pi
{{6, -7, 10}, {0, 3, -1}, {0, 5, -7}}
{{6, -7, 10}, {0, 3, -1}, {0, 5, -7}}*{{1},{3},{5}}
inv {{6, -7, 10}, {0, 3, -1}, {0, 5, -7}}
rank {{6, -11, 13}, {4, -1, 3}, {3, 4, -2}}
2*{{5,1},{-2,3}}+{{1,6},{-2,-2}}
(2*{{5,1},{-2,3}}+{{1,6},{-2,-2}}).{{1},{0}}
x+y+z=1 & x-y-3z=1 & x+2y+z=0
solve x+y+a=k & x-y-3a=1 & x+2y+a=0 for x,y,a
x+y+z=1, x-y-3z=1, x+2y+z=0
inv({{1,1,1},{1,-1,-3},{1,2,1}}).{{1},{1},{0}}
matrix
(1/4, -1/2, 1) * (1/3, 1, -2/3)
(1/4, -1/2, 1) . (1/3, 1, -2/3)
direction (1,1,1)
direction { (1,0,0),(0,1,0),(0,0,1),(1/2,1/2,0),(1,1,1) }
compound interest
continuous interest PV=$3800, rate=6%, periods=5
daily interest, FV=$1200, i=4.5%, n=10
mortgage
mathworld subject finance
y'' + y = 0
y'' + y = 0, y(1)=2, y'(1)=3
d^2/dt^2 s(t) = g, s(0) = 8, s'(0) = 0
{s''(t) = g, s(0) = 8, s'(0) = 5}
dy/dx = x-y, y(-1) = 3
plot y(x) = x + 5 e^(-x - 1) - 1, for -1 <= x <= 5 
slope field of dy/dx = x-y, for -1 <= x <= 5, -2 <= y <= 5
mathworld subject general differential equations
plot z=sin(x)*cos(y)
plot z=sin(x)*cos(y), x=-pi..2*pi, y=-pi/2..2*pi+pi/2
saddle points of z = sin(x)*sin(y)
stationary points (3*x+1)*y^3 + x^2*y
maximize 5 + 3x - 4y - x^2 + x y - y^2
maximize e^x*sin(y) on x^2+y^2=1
minimize e^x*sin(y) on x^2+y^2=1
domain of f(x,y) = log(1-(x^2+y^2))
maximize[{3x+y+z/2, {x+y+z<=4 && 2x+y+z<=6 && 0<=z<=20 && x>=0 && y>=0}}, {x,y,z}]
plot (x-y)^4 + y^4 = 100, -2<x<2, -2<y<2    [ il grafico viene tracciato solo fino ad
        una certa quota - 80 - come posso verificare tracciando le curve di livello: ]
(x-y)^4+y^4=0.5,(x-y)^4+y^4=2,(x-y)^4+y^4=8,(x-y)^4+y^4=32,(x-y)^4+y^4=128 for -2<x<2,-2<y<2
sup (x-y)^4 + y^4 , -2 < x < 2, -2 < y < 2         [ <- infatti il massimo è 272 ]
Fermat's little theorem
Dynamical Systems
Pythagoras tree
Konigsberg theorem
Koch snowflake
Julia set
continuum hypothesis
Riemann zeta function
prime number theorem
Who formulated the halting problem?
continued fraction sqrt(2)
Fourier series expand
Fourier transform exp(-x^2)
mathworld notation
(simboli matematici)

physical constants
physical quantities
laws of physics
scalar
vector
tensor
interest
force
Newton's laws
miscellaneous constants
units and measures
measure
pendulum
red + green + yellow
music
Albert Einstein, Paul Dirac, Richard Feynman
body measurements
grow curve
sun
silver, gold, iron
pear
Social Statistics
Historical Events
biology
natural science
chemistry
music
major scale
intervals C3 Eb3 Bb3 D4 G4 C3 Eb3 Bb3 D4 G4
F#  G G A G C B G G A G D C
genoa
anagrams corde
countries by area
A4
italian
Repubblica Italiana
from Genoa to New York
from Genoa to Turin
from Genoa to Bogliasco
Moon, Genoa
Sun, Genoa
translate integrale from Italian to English
translate integral from English to Italian
students repeating secondary school in Italy
students secondary school in Italy
students in Italy
computer
(seleziona "host information" e clicca "more")
Genoa coordinates
44.4035 North, 8.9725 East
44 deg 24.2' North, 8 deg 58.35' East
44.4047 North, 8.9045 East
44.4088 North, 8.9266 East

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