Find the limit, if it exists, or type dne if it does not exist. a. \displaystyle\lim_{(x, y) \rightarrow (0, 0)} \frac{(x + 23y)^2}{x^2 + 529y^2} =

Suppose we choose a path along the -axis, so that :



On the other hand, let's consider an arbitrary line through the origin, :



The value of the limit then depends on , which means the limit is not the same across all possible paths toward the origin, and so the limit does not exist.