// Welcome to MathStudio! Press enter on your keyboard to evaluate the expressions. Press shift and enter to create a new line.
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1+2+3+4+5
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4*5
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6!
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// Algebra
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x+x+x
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a*a+b+b+b+c*c*c*c
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Expand((a+b)^10)
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Apart((x^2)/(x^2+1)^2)
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Factor(x^4+5x^2-6)
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// Solving Quadratic Equations
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Solve(x^2+5x+6=0)
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Solve(1,5,6)
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// Limits
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Limit((3x-15)/sqrt(x^2-10x+25), x, 5, 1)
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Limit(cos(a*x)/x^2-cos(b*x)/x^2, x, 0)
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// Derivatives
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D(sin(x))
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D(sin(x)*cos(x^2))
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D(f(x)*g(x))
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D(sqrt(x)^sqrt(x), x)
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// Integrals
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Integrate(x^2+3x-6)
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Integrate(exp(x)*sin(x))
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Integrate(-3/x^2+sin(x)/(1-sin(x)))
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Integrate((1+2cos(x))/(1+2sin(x)))
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Integrate(1/(a*x^2+b*x), x)
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// Graphing
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Plot(sin(x))
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Plot(sin(x),cos(x),colors=[blue,red])
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Plot(sin(x^2)*x)
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Plot(sin(x),lineWidth=5,lineDash=[10,5])
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// Parametric Plots
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ParametricPlot(cos(u),sin(u))
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ParametricPlot(sin(7u), sin(8u), u=[0,2@pi,400], color=blue, numbers=0)
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ParametricPlot(10sin(31u), 10cos(31u), u=[0,2@pi,48], axis=0, numbers=0, color=orange)
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// Polar Plots
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PolarPlot(sin(2@theta))
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PolarPlot(@e^sin(@theta)-2cos(4@theta)+sin(1/24(-@pi+2@theta))^5, @theta=[0,21@pi,1000], color=magenta)
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PolarPlot(2-2*sin(@theta)+sin(@theta)*sqrt(abs(cos(@theta)))/(sin(@theta)+1.4),color=red,shade=middle)
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// Time Graphing
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Plot(sin(x+T))
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Plot(sin(x+T)*x)
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Plot(sin(x+T),x*cos(T)+sin(T))
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// Vector Fields
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VectorPlot(-y, x)
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VectorPlot(-y, cos(x+T))
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// Multiple Plots
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1Plot(sin(x), color=blue)
2ParametricPlot(cos(u), sin(u), color=red)
3PolarPlot(sin(2@theta), color=green)
4ParametricPlot(2cos(u), 2sin(u), color=magenta)
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// Minimum, Maximum and Zero Values
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Plot(sin(x),min=1)
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Plot(cos(x),sin(x),color=[blue,red],min=[0,1],max=[1,0])
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// List Plots
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ListPlot([1,2,3,4,5,4,3,8,6,8])
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ListPlot(Random(1,10,100), lines=0, points=4, shade=0, color=red)
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// Regression Analysis
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LinearFit([1,4,9,5,7,5,4,2,9], [3,4,5,7,8,10,4,7,6])
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LinearFitModel([1,4,9,5,7,5,4,2,9], [3,4,5,7,8,10,4,7,6])
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LinearFitPlot([1,4,9,5,7,5,4,2,9], [3,4,5,7,8,10,4,7,6])
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QuadraticFitPlot([7, 5, 8, 10, 13], [15, 19, 14, 18, 25])
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SinFitPlot(sin((1:50)/5)*Random(1,3,50))
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// 3D Graphing
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Plot3D(2cos(x)*sin(y))
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Plot3D(cos(x)*y+sin(y)*x, colors=[red, yellow])
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1Slider(a,2,10,0.1)
2Plot3D(cos(x)+sin(y),x=[-a,a],y=[-a,a])
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Plot3D(sin(T-sqrt(x^2+y^2)), colors=[red, yellow], lines=0)
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// 3D Parametric Plots
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ParametricPlot3D((3+sin(v)+cos(u))*sin(2v), (3+sin(v)+cos(u))*cos(2v), sin(u)+2cos(v), u=[0, 2@pi, 40], v=[0, 2@pi, 80], lines=0, name=Toroid)
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// Sliders
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1Slider(n, 1..50)
2Expand((a+b)^n)
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1Slider(n, 1..100)
2(1:n)^2
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1Slider(a, 1, 10, 0.1)
2Plot(sin(a*x))
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1Slider(a, 1, 10, .1)
2Slider(b, 0, 10, .1)
3Slider(c, 1, 10, .1)
4Plot(sin(a*x+b)*c)
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1Slider([a,b],1,10,0.1)
2Plot3D(cos(a*x)+sin(b*y))
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// Scripting
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1one = 1
2two = 2
3three = 3
4one + two + three
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one^2 + two^2 + three^2
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1cube(x) = x^3
2cube(5)
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1data = @[29, 29]
2for [row, column] in data
3 data(row, column) = gcd(row, column) > 1
4end
5ImagePlot(data)
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// Lists
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1:100
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[1,2,3]*[4,5,6]
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// Matrices
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[[1,2],[3,4]]*[[5,6],[7,8]]
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Inverse([[1,5,6], [2,4,5], [1,1,7]])
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Inverse([[a,b], [c,d]])
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Identity(5)
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// Units
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2@feet+24@inches
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2@miles+4@kilometers
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(40@miles/@hour)*3@hours
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@megabytes -> @bytes
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50@fahrenheit -> @celsius
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2@hours -> @s
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5@years -> @days
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@inches -> @nanometers
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@tbsp -> @tsp
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@kilogram -> @pound
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4@miles -> @inches
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991
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