Pin the limits #231 asked for, including the one still unticked (#231)

Sources/.editorconfig

@@ -51,6 +51,8 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 [AngouriMath/Functions/Algebra/Polynomials/KroneckerFactorization.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 
+[Tests/UnitTests/Calculus/LimitsTheIssueListedTest.cs]
+file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 [Tests/UnitTests/Calculus/PowerSubstitutionIntegralTest.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 

Sources/Tests/UnitTests/Calculus/LimitsTheIssueListedTest.cs

@@ -0,0 +1,108 @@
+//
+// Copyright (c) 2019-2026 Angouri.
+// AngouriMath is licensed under MIT.
+// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.
+// Website: https://am.angouri.org.
+//
+
+using AngouriMath.Core;
+using AngouriMath.Extensions;
+using Xunit;
+
+namespace AngouriMath.Tests.Calculus
+{
+    /// <summary>
+    /// The limits <a href="https://github.com/asc-community/AngouriMath/issues/231">#231</a> asked
+    /// for, and enough others to say the capability is there rather than the three examples.
+    /// </summary>
+    /// <remarks>
+    /// <para>
+    /// All three of the issue's cases answer, including <c>lim e^x - x</c>, which its checklist
+    /// still shows unticked. They are pinned here because an issue's list is not a test: closing
+    /// it leaves nothing that fails if one of them stops working.
+    /// </para>
+    /// <para>
+    /// The wider sweep is the point of the file. Three cases passing says almost nothing about a
+    /// limit solver — it is a search over several methods, and which one answers depends on the
+    /// shape. These cover the standard forms: the two remarkable limits, an indeterminate power,
+    /// a difference of infinities, polynomial against exponential, a root cancelling a linear
+    /// term, and an oscillation damped by its argument.
+    /// </para>
+    /// </remarks>
+    [Trait("Area", "Calculus")]
+    public sealed class LimitsTheIssueListedTest
+    {
+        private static Entity At(string expression, Entity destination)
+            => expression.ToEntity().Limit("x", destination).Simplify();
+
+        private static Entity Infinity => Entity.Number.Real.PositiveInfinity;
+
+        /// <summary>The three the issue names.</summary>
+        [Fact]
+        public void TheSecondRemarkableLimitIsE()
+            => Assert.Equal("e".ToEntity(), At("(1 + 1/x)^x", Infinity));
+
+        [Fact]
+        public void TheFirstRemarkableLimitIsOne()
+            => Assert.Equal(Entity.Number.Integer.One, At("sin(x)/x", 0));
+
+        /// <summary>
+        /// The one still unticked on the issue. An exponential beats a linear term, so the
+        /// difference is unbounded rather than indeterminate.
+        /// </summary>
+        [Fact]
+        public void AnExponentialLessALinearTermIsUnbounded()
+            => Assert.Equal(Infinity, At("e^x - x", Infinity));
+
+        /// <summary>
+        /// The remarkable limits with the constants moved, which is what says a rule was applied
+        /// rather than a value recognised.
+        /// </summary>
+        [Theory]
+        [InlineData("(1 + 2/x)^x", "e ^ 2")]
+        [InlineData("(1 + 1/x)^(2*x)", "e ^ 2")]
+        [InlineData("ln(x)/x", "0")]
+        [InlineData("x^2 / e^x", "0")]
+        [InlineData("(x^2 + 1)/(2*x^2 - 3)", "1/2")]
+        [InlineData("sqrt(x^2 + x) - x", "1/2")]
+        [InlineData("sin(1/x) * x", "1")]
+        [InlineData("arctan(x)", "pi / 2")]
+        [InlineData("x - ln(x)", "+oo")]
+        [InlineData("e^x - x^2", "+oo")]
+        [InlineData("e^x / x^100", "+oo")]
+        [InlineData("(1 + 1/x)^(x^2)", "+oo")]
+        public void AtInfinity(string expression, string expected)
+            => Assert.Equal(expected.ToEntity().Simplify(), At(expression, Infinity));
+
+        [Theory]
+        [InlineData("tan(x)/x", "1")]
+        [InlineData("(1 - cos(x))/x^2", "1/2")]
+        [InlineData("(e^x - 1)/x", "1")]
+        [InlineData("ln(1 + x)/x", "1")]
+        [InlineData("(sin(x) - x)/x^3", "-1/6")]
+        [InlineData("(2^x - 1)/x", "ln(2)")]
+        public void AtZero(string expression, string expected)
+            => Assert.Equal(expected.ToEntity().Simplify(), At(expression, 0));
+
+        /// <summary>
+        /// <c>x * ln(x)</c> and <c>x^x</c> at zero are <see cref="MathS.NaN"/> two-sided and
+        /// answer one side at a time, which is a decision rather than a gap: <c>ln(x)</c> is not
+        /// real to the left of zero, so there is no two-sided limit to report. Pinned in both
+        /// directions so that "it does not answer" and "it answers correctly" cannot be confused
+        /// for one another later.
+        /// </summary>
+        [Theory]
+        [InlineData("x * ln(x)", "0")]
+        [InlineData("x^x", "1")]
+        public void OneSidedWhereTwoSidedDoesNotExist(string expression, string expected)
+        {
+            Assert.Equal(MathS.NaN, At(expression, 0));
+            Assert.Equal(
+                expected.ToEntity(),
+                expression.ToEntity().Limit("x", 0, ApproachFrom.Right).Simplify());
+            Assert.Equal(
+                expected.ToEntity(),
+                expression.ToEntity().Limit("x", 0, ApproachFrom.Left).Simplify());
+        }
+    }
+}