[Copyright 2024 Quantum Software Development. Code released under the MIT License license.](https://github.com/Quantum-Software-Development/Math/blob/3bf8270ca09d3848f2bf22f9ac89368e52a2fb66/LICENSE)
+The given function is a polynomial function of the form:
+$$f(x)=axn+bxn−1+cxn−2+...+dx+e$$
-
+
+As x approaches infinity, the highest power of x in the function dominates the value of the function. This means that we can ignore all the lower-order terms, and simply consider the behavior of the highest-order term.
+In this case, the highest-order term is 2x4. As x approaches infinity, x4 also approaches infinity, and so the function f(x) also approaches infinity.
+Therefore, the limit of the function as x approaches infinity is infinity. We can write this mathematically as:
+$$x→∞lim x32x4−3x3+x+6 =0$$
+#
+### 3b:Finding the limit of a rational function as x approaches infinity
-
+The given function is a rational function of the form
+$$f(x)=cxm+fxm−1+...+gx+haxn+bxn−1+...+dx+e$$
+
+, where n > m. As x approaches infinity, the highest power of x in the numerator dominates the value of the numerator, and the highest power of x in the denominator dominates the value of the denominator. This means that we can ignore all the lower-order terms, and simply consider the behavior of the highest-order terms.
+In this case, the highest-order term in the numerator is 2x4, and the highest-order term in the denominator is x3.
+As x approaches infinity, 2x4 grows much faster than x3, and so the function f(x) approaches zero.
+#
+### These processes above demonstrates how limits help us understand the behavior of functions near points that might not be defined, by finding equivalent expressions that are easier to evaluate.
+#
+######
[Copyright 2024 Quantum Software Development. Code released under the MIT License license.](https://github.com/Quantum-Software-Development/Math/blob/3bf8270ca09d3848f2bf22f9ac89368e52a2fb66/LICENSE) + + @@ -310,47 +327,25 @@ Even though ( x ) is negative, y. -