Final answer:
To find the limit of the given expression, substitute the values of x and y and simplify. If the result is an indeterminate form, use other techniques to find the limit.
Step-by-step explanation:
To find the limit of the given expression, we need to substitute the values of x and y into the expression and simplify:
lim_(x,y)→(0,0) (x^4 - 4y^2)/(x^2 + 2y^2)
Substituting x = 0 and y = 0:
lim_(x,y)→(0,0) (0^4 - 4(0)^2)/(0^2 + 2(0)^2)
Simplifying:
lim_(x,y)→(0,0) 0/0
Since we get an indeterminate form of 0/0, we need to use other techniques such as L'Hospital's Rule or factoring and canceling common factors to find the limit.