Evaluate `lim_(xtooo) sqrt(x)(sqrt(x+c)-sqrt(x)).`

Explanation

To evaluate the limit \( \lim_{x \to \infty} \sqrt{x} (\sqrt{x+c} - \sqrt{x}) \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the limit:
\[ \lim_{x \to \infty} \sqrt{x} (\sqrt{x+c} - \sqrt{x}) \]

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