We are asked to find the limit of the function $x^2 + xe^x$ as $x$ approaches infinity. That is, we need to find $A = \lim_{x \to \infty} (x^2 + xe^x)$.

1. Problem Description

We are asked to find the limit of the function $x^2 + xe^x$ as $x$ approaches infinity. That is, we need to find $A = \lim_{x \to \infty} (x^2 + xe^x)$.

2. Solution Steps

We need to evaluate the limit of the function $x^2 + xe^x$ as $x$ approaches infinity.

Since $x^2$ and $xe^x$ both tend to infinity as $x$ goes to infinity, we can consider them separately and then add the results. Specifically,

$\lim_{x \to \infty} x^2 = \infty$.

Also, $\lim_{x \to \infty} xe^x = \infty$.

Therefore, $\lim_{x \to \infty} (x^2 + xe^x) = \lim_{x \to \infty} x^2 + \lim_{x \to \infty} xe^x = \infty + \infty = \infty$.

More formally, since both terms go to infinity as $x$ approaches infinity, their sum also goes to infinity.

3. Final Answer

$\infty$