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The given function is:

\[
f(n, y) = \lim_{n \to 2, y \to 2} \frac{n^2 + ny + n + y}{n + y}
\]

Let's compute the limit as \(n \to 2\) and \(y \to 2\). First, substitute \(n = 2\) and \(y = 2\) directly into the function:

\[
\frac{n^2 + ny + n + y}{n + y}
\]

Substituting \(n = 2\) and \(y = 2\):

\[
= \frac{2^2 + 2(2) + 2 + 2}{2 + 2}
= \frac{4 + 4 + 2 + 2}{4}
= \frac{12}{4}
= 3
\]

Therefore, the value of the limit is:

\[
f(n, y) = 3
\]

Would you like more details on any specific steps?

Here are 5 related questions to explore further:
1. How do you compute limits of multivariable functions in general?
2. What happens if a limit doesn't exist for some function?
3. How would the limit change if the function was undefined at a specific point?
4. Can you find limits at infinity for this function?
5. How does L'Hôpital's rule apply in solving indeterminate limits?

**Tip:** When calculating limits of multivariable functions, always check if you can directly substitute the variables, or if simplifying the expression first might help avoid indeterminate forms.

Find the limit of the function f(n, y) as n approaches 2 and y approaches 2 for f(n, y) = (n^2 + ny + n + y) / (n + y).

This problem involves calculating the limit of a multivariable function f(n, y) as n approaches 2 and y approaches 2. By directly substituting values into the function, we simplify the expression and find the limit to be 3. This solution highlights key concepts in multivariable calculus, including limits and the substitution method.

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