AngouriMath
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AsAPowerOfTheVariable(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
A power of the reciprocal of the variable as a power of the variable: (1/x)^p as
x^(-p), and (-1/x)^p as (-1)^p * x^(-p).
x^(-p), and (-1/x)^p as (-1)^p * x^(-p).
Remarks
Exact on the way to +oo, where x is real and positive, and on the principal branch
for any exponent. A one-sided limit at 0 is taken by putting 0 + 1/x or 0 - 1/x for
x, so these are what the root of the variable turns into, and nothing rewrites them:
x^3 * sqrt(1/x) / (x^2 * (1/x)^(-1/2)), which is 1, took 1.6 s, l'Hopital's rule
differentiating it sixteen deep, and lim x->0+ ln(x) / ln(sqrt(x)) asked it eight
times on the way to 2 and took 16 s.
for any exponent. A one-sided limit at 0 is taken by putting 0 + 1/x or 0 - 1/x for
x, so these are what the root of the variable turns into, and nothing rewrites them:
x^3 * sqrt(1/x) / (x^2 * (1/x)^(-1/2)), which is 1, took 1.6 s, l'Hopital's rule
differentiating it sixteen deep, and lim x->0+ ln(x) / ln(sqrt(x)) asked it eight
times on the way to 2 and took 16 s.
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