Since all paths we've tried have limit 0, it's reasonable to suspect the limit might exist and equal 0. To prove this assertion, we can use the Squeeze Theorem, which states that if g(x) ≤ f(x) ≤ h(x) for every x in an interval, and if lim x → a g(x) = lim x → a h(x) = L for a point a in the interval, then lim x → a f(x) = L.