Find the limit of the sequence, using L'Hôpital's rule when appropriate. \[ \frac{\sqrt{n}}{\sqrt{n+4}} \]

Step 1 ：We are given the sequence \(\frac{\sqrt{n}}{\sqrt{n+4}}\) and asked to find its limit as n approaches infinity.

Step 2 ：This sequence is in the form of \(\frac{\infty}{\infty}\) as n approaches infinity, so we can apply L'Hôpital's rule.

Step 3 ：L'Hôpital's rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

Step 4 ：Before we can apply L'Hôpital's rule, we need to differentiate the numerator and the denominator.

Step 5 ：The derivative of the numerator, \(\sqrt{n}\), is \(\frac{1}{2\sqrt{n}}\).

Step 6 ：The derivative of the denominator, \(\sqrt{n + 4}\), is \(\frac{1}{2\sqrt{n + 4}}\).

Step 7 ：Applying L'Hôpital's rule, we find that the limit of the sequence is the limit of the quotient of these derivatives, which is 1.

Step 8 ：Final Answer: The limit of the sequence is \(\boxed{1}\).