Algebraic and Analytic Methods - 1.4 Calculus of One Variable

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
1.4.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(2)}(x) = \deriv[2]{f}{x}}
f^{(2)}(x) = \deriv[2]{f}{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(f(x))^(2) = diff(f, [x$(2)])

(f[x])^(2) == D[f, {x, 2}]
Failure Failure
Failed [30 / 30]
Result: .7500000006+1.299038106*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5}


Result: .2500000002+.4330127020*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = .5}


Result: 1.000000001+1.732050808*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 2}


Result: -.7500000006-1.299038106*I
Test Values: {f = -1/2+1/2*I*3^(1/2), x = 1.5}

... skip entries to safe data
Failed [30 / 30]
Result: Complex[0.7500000000000002, 1.299038105676658]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}


Result: Complex[0.25000000000000006, 0.4330127018922193]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]}

... skip entries to safe data
1.4.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)}
\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(f, [x$(2)]) = diff(diff(f, x), x)

D[f, {x, 2}] == D[D[f, x], x]
Successful Successful Skip - symbolical successful subtest Successful [Tested: 30]
1.4.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)}
f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(f(x))^(n) = diff((f(x))^(n - 1), x)

(f[x])^(n) == D[(f[x])^(n - 1), x]
Failure Failure
Failed [84 / 90]
Result: .299038106+.7500000000*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 1}


Result: -.1160254034+.7990381060*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 2}


Result: -.4999999999+.6339745980*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 3}


Result: -.5669872980+.2500000000*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = .5, n = 1}

... skip entries to safe data
Failed [84 / 90]
Result: Complex[0.299038105676658, 0.7499999999999999]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}


Result: Complex[-0.11602540378443849, 0.799038105676658]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]}

... skip entries to safe data
1.4.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}}
\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
int(f*g, x) = (int(f, x))*g - int((int(f, x))*diff(g, x), x)

Integrate[f*g, x, GenerateConditions->None] == (Integrate[f, x, GenerateConditions->None])*g - Integrate[(Integrate[f, x, GenerateConditions->None])*D[g, x], x, GenerateConditions->None]
Successful Successful - Successful [Tested: 100]
1.4.E36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{n} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}}
R_{n} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a < c, c < x} 
R[n] = ((f(c))^(n + 1))/(factorial(n + 1))*(x - a)^(n + 1)
 
Subscript[R, n] == Divide[(f[c])^(n + 1),(n + 1)!]*(x - a)^(n + 1)
 Skipped - no semantic math Skipped - no semantic math - -
1.4.E37 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t}}
R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
R[n] = (1)/(factorial(n))*int((x - t)^(n)* (f(t))^(n + 1), t = a..x)

Subscript[R, n] == Divide[1,(n)!]*Integrate[(x - t)^(n)* (f[t])^(n + 1), {t, a, x}, GenerateConditions->None]
Failure Failure
Failed [300 / 300]
Result: 1.991025404+2.448557159*I
Test Values: {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 1}


Result: .8660254040+3.875000000*I
Test Values: {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 2}


Result: -.6527245960+3.130552164*I
Test Values: {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 3}


Result: .6250000000+2.814582563*I
Test Values: {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = -1/2+1/2*I*3^(1/2), n = 1}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[1.9910254037844388, 2.4485571585149866]
Test Values: {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.8660254037844387, 3.875]
Test Values: {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
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