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Question
Evaluate `lim_((x, y) -> (0, 0)) cos((x^3 + y^2)/(x + y + 2))` If the limits exists
Solution
`lim_((x, y) -> (0, 0)) cos((x^3 + y^2)/(x + y + 2))`
Let us take y = 0 for f(y), then
`lim_(y -> 0) cos(y^2/(y + 2)) = 1 ≠ oo`
∴ Limit exists
Now, `lim_((x, y) -> (0, 0)) cos((x^3 + y^2)/(x + y + 2))`
= `cos(0/2)`
= cos (0)
= 1
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