Evaluate `lim_(ntooo) nsin(2pisqrt(1+n^(2))),(n inN).`

Explanation

To evaluate the limit \( \lim_{n \to \infty} n \sin(2\pi \sqrt{1+n^2}) \), we can follow these steps:

### Step 1: Rewrite the Expression
We start with the limit:
\[ \lim_{n \to \infty} n \sin(2\pi \sqrt{1+n^2}). \]
We can simplify the argument of the sine function. Notice that as \( n \) becomes very large, \( \sqrt{1+n^2} \) can be approximated as:
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