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प्रश्न
Let f(x, y) = `(y^2 - xy)/(sqrt(x) - sqrt(y))` for (x, y) ≠ (0, 0). Show that `lim_((x, y) -> (0, 0)) "f"(x, y)` = 0
उत्तर
`lim_((x, y) -> (0, 0)) "f"(x, y) = lim_((x, y) -> (0, 0)) (y^2 - xy)/(sqrt(x) - sqrt(y))`
= `lim_((x, y)-> (0, 0)) (y^2 - xy)/(sqrt(x) - sqrt(y)) xx (sqrt(x) + sqrt(y))/(sqrt(x) + sqrt(y))`
= `lim_((x, y) -> (0, 0)) (-y(x - y)(sqrt(x) + sqrt(y)))/((x - y))`
= `lim_((x, y) -> (0, 0)) - y(sqrt(x) + sqrt(y))` = 0
Hence proved.
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