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Question
Evaluate `lim_((x, y) -> (1, 2)) "g"(x, y)`, if the limit exists, where `"g"(x, y) = (3x2 - xy)/(x^2 + y^2 + 3)`
Solution
`lim_((x, y) -> (1, 2)) "g"(x, y)`
= `lim_((x, y) -> (1 , 2)) (3x^2 - xy)/(x^2 + y^2 + 3)`
= `(lim_((x, y) -> (1, 2)) 3x^2 - xy)/(lim_((x, y) -> (1, 2)) x^2 + y^2 + 3)`
= `(3(1)^2 - (1)(2))/((1)^2 + (2)^2 + 3)`
= `(3 - 2)/(1 + 4 + 3)`
= `1/8`
If `lim_((x, y) -> ("a", "b")) "f"("a", "b") = "f"("a", "b")` then the limit exists.
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