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प्रश्न
Evaluate `lim_((x, y) -> (0, 0)) cos(("e"^x sin y)/y)`, if the limit exists
उत्तर
`lim_((x, y) -> (0, 0)) cos(("e"^x sin y)/y)`
Using two different parts to approach the point along x = 0 and y = 0
`lim_((x, y) -> (0, 0)) cos(("e"^x sin y)/y)`
= `cos(lim_((x, y)-> (0, 0)) ("e"^x sin y)/y)`
= cos (1) ........`(because lim_(y -> 0) siny/y = 1)`
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