Evaluate, `lim_(xtosqrt(2)) (x^(4)-4)/(x^(2)+3sqrt(2)x-8)`.

Explanation

To evaluate the limit \( \lim_{x \to \sqrt{2}} \frac{x^4 - 4}{x^2 + 3\sqrt{2}x - 8} \), we will follow these steps:

### Step 1: Substitute \( x = \sqrt{2} \)
First, we substitute \( x = \sqrt{2} \) into the expression to check if we get an indeterminate form.

\[ \text{Numerator: } (\sqrt{2})^4 - 4 = 4 - 4 = 0 \]
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