Final answer:
To find the limit of a function as (x, y) approaches (0,0) along the line y = x/2, we substitute y with x/2 into the function and take the limit as x approaches 0. A specific limit can't be provided without the actual function f(x, y). An example approach was demonstrated with a hypothetical function.
Step-by-step explanation:
To find the limit of the function f(x, y) as (x, y) approaches (0,0) along the line y = x/2, we will substitute y with x/2 in the expression for f(x, y) and then take the limit as x approaches 0. However, as the function f(x, y) itself is not provided in the question, we cannot give a specific answer.
Generally, the procedure involves plugging in x/2 for y into the function, simplifying, and then using limit properties to find the result as x goes to 0. This approach helps in determining whether the limit exists and what the limit is along the specified path.
For example, if f(x, y) = x^2 + y^2, then along the line y = x/2, the function becomes f(x, x/2) = x^2 + (x/2)^2 = (5/4)x^2. The limit as x approaches 0 is then 0 because (5/4)x^2 also approaches 0 as x approaches 0.