// (lim x->0) (x*sin(x) - x*sin(x)) / 1 = 0
public void CalculateLimit_AndReturnsCorrectLimit_11()
{
var numerator = new List <Summand>
{
new Summand
{
PolynomialDegree = 1,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1
}
}
},
new Summand
{
Coefficient = -1,
PolynomialDegree = 1,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1
}
}
}
};
var denominator = new List <Summand>
{
new Summand()
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0);
}
// (lim x->1) sin(7Pi*x)/sin(2Pi*x) = -7/2
public void CalculateLimit_MKD_69_34()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 7 * Math.PI
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 2 * Math.PI
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 1);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(-3.5);
}
// (lim x->0) cos(x) - 1 / x^2 = -1/2
public void Calculate_Antano_Limit_10_cos()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Cosine {
Aparam = 1, Bparam = 0
}
}
},
new Summand
{
Coefficient = -1.0,
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 2
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(-0.5);
}
// x->-1 (x^3+1)/sin(x+1)
public void Kuznecov_15_3()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 3
},
new Summand
{
Coefficient = 1.0,
},
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1.0, Bparam = 1.0
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, -1);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(3.0);
}
// (lim x->1) 5x-x^0.5 = 4
public void CalculatePoviloLimit1()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = -1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1, Bparam = 0, PowerNumerator = 1, PowerDenominator = 2
}
}
},
new Summand
{
Coefficient = 5.0,
PolynomialDegree = 1,
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 1);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(4);
}
// (lim x->0)(x) / ((4-x)^1/2)-2 = -4
public void Calculate_Antano_Limit_4()
{
var numerator = new List <Summand>
{
new Summand
{
PolynomialDegree = 1,
Coefficient = 1.0
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = -1, Bparam = 4, PowerNumerator = 1, PowerDenominator = 2
}
}
},
new Summand
{
Coefficient = -2.0
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(-4.0);
}
// (lim x->0) ((32+x)^(1/5) - 2) / x = 1/80
public void CalculateLimit_MKD_74_5()
{
var numerator = new List <Summand>
{
new Summand
{
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction
{
Aparam = 1, Bparam = 32, PowerNumerator = 1, PowerDenominator = 5
}
}
},
new Summand
{
Coefficient = -2
}
};
var denominator = new List <Summand>
{
new Summand
{
PolynomialDegree = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(1.0 / 80);
}
// (lim x->-2/Pi) 1 - cos(Pi*x + 2) = 0
public void CalculateLimit_MKD_67_16()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1
},
new Summand
{
Coefficient = -1,
Multiplicands = new List <IElementaryFunction>
{
new Cosine {
Aparam = Math.PI, Bparam = 2
}
}
},
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, -2 / Math.PI);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0);
}
// (lim x->-1/3) (9*x^2 - 1) / (x + 1/3) = -6
public void CalculateLimit_MKD_67_6()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 9,
PolynomialDegree = 2
},
new Summand
{
Coefficient = -1
},
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 1.0 / 3
},
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, -1.0 / 3);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(-6.0);
}
// (lim x->0) (x^(1/5)) / (x^(1/3)) = +INF
public void CalculateLimit_AndReturnsCorrectLimit_9()
{
var numerator = new List <Summand>
{
new Summand
{
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction()
{
Aparam = 1, PowerNumerator = 1, PowerDenominator = 5
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1, PowerNumerator = 1, PowerDenominator = 3
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.PositiveInfinity);
}
// (lim x->0) sin (x + 3) = sin(3) ~ 0.141120008059867
public void CalculateLimit_AndReturnsCorrectLimit_5()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine()
{
Aparam = 1.0,
Bparam = 3
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
MathHelper.AreApproximatelyEqual(result.Value, 0.141, 0.005).Should().BeTrue();
}
// (lim x->0) sin(4*x) / x
public void CalculateLimit_MKD_69_26()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 4
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0.0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(4);
}
// (lim x->0) x / 2^x = 0
public void Calculate_Antano_Limit_9_EX()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 1
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new ExponentialFunction {
Aparam = 2, Bparam = 0
},
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0);
}
// tg(x) replaced with sin(x) / cos(x)
// (lim x->0) (cos(x) * (e^(7x) - e^(2x))) / sin(x) = 5
public void CalculateLimit_MKD_69_33()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Cosine {
Aparam = 1
}
},
SumsRaisedToPower = new List <SumRaisedToPower>
{
new SumRaisedToPower
{
Degree = 1,
Sum = new List <Summand>
{
new Summand
{
Coefficient = 1,
Multiplicands = new List <IElementaryFunction>
{
new ExponentialFunction {
Aparam = 7
}
}
},
new Summand
{
Coefficient = -1,
Multiplicands = new List <IElementaryFunction>
{
new ExponentialFunction {
Aparam = 2
}
}
}
}
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0.0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(5);
}
// (lim x->0)
public void CalculateLimit_MKD_68_14()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1.0, Bparam = 1.0, PowerNumerator = 1, PowerDenominator = 2
}
},
SumsRaisedToPower = new List <SumRaisedToPower>
{
new SumRaisedToPower
{
Degree = 1,
Sum = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1.0, Bparam = 1.0, PowerNumerator = 1, PowerDenominator = 2
},
}
},
new Summand
{
Coefficient = -1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = -1.0, Bparam = 1.0, PowerNumerator = 1, PowerDenominator = 2
},
}
}
}
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1.0, Bparam = 0, PowerNumerator = 1, PowerDenominator = 5
},
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0.0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0.0);
}
//x->0 (1+x*sinx-cos2x)/sin^2(x)
public void Kuznecov_15_2()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0
},
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1.0, Bparam = 0
}
},
PolynomialDegree = 1
},
new Summand
{
Coefficient = -1.0,
Multiplicands = new List <IElementaryFunction>
{
new Cosine {
Aparam = 2.0, Bparam = 0
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1,
SumsRaisedToPower = new List <SumRaisedToPower>
{
new SumRaisedToPower
{
Degree = 2,
Sum = new List <Summand>
{
new Summand
{
Coefficient = 1,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1.0, Bparam = 0
}
}
}
}
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(3.0);
}
// (lim x->0) (((1 + x)^3) - ((1 + 3x)^1)) / (x + x^5) = 0
public void CalculateLimit_AndReturnsCorrectLimit_2()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
SumsRaisedToPower = new List <SumRaisedToPower>
{
new SumRaisedToPower
{
Degree = 3,
Sum = new List <Summand>
{
new Summand {
Coefficient = 1.0
},
new Summand {
Coefficient = 1.0, PolynomialDegree = 1
}
}
}
}
},
new Summand
{
Coefficient = -1.0,
SumsRaisedToPower = new List <SumRaisedToPower>
{
new SumRaisedToPower
{
Degree = 1,
Sum = new List <Summand>
{
new Summand {
Coefficient = 1.0
},
new Summand {
Coefficient = 3.0, PolynomialDegree = 1
}
}
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 5
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0.0);
}
