The problem asks to evaluate the limit of the expression $x^2 + xe^x$ as $x$ approaches $0$. That is, we need to find $\lim_{x \to 0} (x^2 + xe^x)$.

1. Problem Description

The problem asks to evaluate the limit of the expression $x^2 + xe^x$ as $x$ approaches $0$.

That is, we need to find $\lim_{x \to 0} (x^2 + xe^x)$.

2. Solution Steps

To find the limit, we can substitute $x = 0$ directly into the expression since it is a continuous function.

$\lim_{x \to 0} (x^2 + xe^x) = (0)^2 + (0)e^0$

We know that $0^2 = 0$ and $e^0 = 1$. Thus,

$\lim_{x \to 0} (x^2 + xe^x) = 0 + 0(1) = 0 + 0 = 0$

3. Final Answer

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