Question

find the limit (if it exists). (if an answer does not exist, enter dne.)
\\(\lim_{(x,y)\to(1,5)}\frac{xy - 5}{xy+5}\\)

Explanation:

Step1: Substitute values

Let \(x = 1\) and \(y = 5\) into the function \(\frac{xy - 5}{xy+5}\).
We get \(\frac{1\times5 - 5}{1\times5+5}\).

Step2: Simplify the expression

First, calculate the numerator: \(1\times5 - 5=5 - 5 = 0\).
Then, calculate the denominator: \(1\times5+5=5 + 5=10\).
So the fraction is \(\frac{0}{10}=0\).

Answer:

0