Final answer:
Without the specific function f(x,y), the partial derivatives ∂z/∂x and ∂z/∂y at the point (0, 0) using the limit definition cannot be calculated. The process involves evaluating the limit of the difference quotient as h approaches zero for both x and y separately.
Step-by-step explanation:
To find the partial derivatives ∂z/∂x and ∂z/∂y at the point (0, 0) using the limit definition of partial derivatives, we must assume a function z = f(x,y) is defined around that point. The limit definition of a partial derivative with respect to x is:
∂z/∂x = lim(h→ 0) [f(x+h, y) - f(x, y)]/h.
Similarly, the partial derivative with respect to y is:
∂z/∂y = lim(h→ 0) [f(x, y+h) - f(x, y)]/h.
Without the specific function, we cannot compute the actual values. However, this process involves substituting x = 0 and y = 0 into the respective expressions and taking the limit as h approaches zero. If there was a typo and an actual function was meant to be provided, please resubmit the question with the correct function.