Final answer:
The limit of the expression 5xy⁴x²y⁸ as (x,y) approaches (0,0) is 0.
Step-by-step explanation:
To find the limit of the given expression, we can use the properties of limits and simplify the expression as much as possible.
The given expression is 5xy⁴x²y⁸. As (x,y) approaches (0,0), notice that both x and y approach 0. Therefore, we can substitute 0 for both x and y in the expression.
Substituting 0 for x and y in the expression gives us 5(0)(0⁴)(0²)(0⁸), which simplifies to 0.
The limit of the expression 5xy⁴x²y⁸ as (x,y) approaches (0,0) is 0.