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We are tasked with evaluating the following function's limits:

\[
f(x) = x \sqrt{2 + x^2}
\]

at three points:
- (a) \(\lim\limits_{x \to 0^-} f(x)\)
- (b) \(\lim\limits_{x \to 0^+} f(x)\)
- (c) \(\lim\limits_{x \to 0} f(x)\)

### Solution Approach:

1. **(a) Limit as \(x \to 0^-\)**:
   - The function is continuous, and as \(x\) approaches 0 from the left (\(x \to 0^-\)), the behavior of the square root term does not change because it involves \(x^2\), which is non-negative.
   - Thus, we can directly substitute \(x = 0\) into the function.
   
   \[
   \lim_{x \to 0^-} x \sqrt{2 + x^2} = 0 \cdot \sqrt{2 + 0^

Evaluate the limits of the function f(x) = x√(2 + x²) as x approaches 0 from the left, from the right, and as x approaches 0 directly.

This problem involves evaluating the left-hand limit, right-hand limit, and two-sided limit of the function f(x) = x√(2 + x²) as x approaches 0. It explores key calculus concepts like continuity and the behavior of functions near critical points.

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