Final answer:
The limit of the function (x+3y)/(x+2y) as x and y approach (3,2) is simply the substitution of these values into the function, which gives us a limit of 9/7.
Step-by-step explanation:
The question is asking to solve a limit problem as both variables x and y approach certain values. To solve the limit lim_(x, y) →(3,2)(x+3y)/(x+2y), we can simply substitute the values of x and y into the function since the function seems to be continuous at the point (3, 2). This means we will replace x with 3 and y with 2 in the expression. So, the calculation would be as follows:
((3) + 3(2)) / ((3) + 2(2)) = (3 + 6) / (3 + 4) = 9 / 7.
Therefore, the limit is 9/7.