DylanM7276 DylanM7276
  • 10-10-2019
  • Mathematics
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Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y)→(2, 2) e^āˆ’ xy cos(x + y)

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LammettHash
LammettHash LammettHash
  • 10-10-2019

[tex]e^{-xy}\cos(x+y)[/tex] is continuous everywhere because the component functions [tex]e^{-x}[/tex] and [tex]\cos x[/tex] are continuous. So

[tex]\displaystyle\lim_{(x,y)\to(2,2)}e^{-xy}\cos(x+y)=e^{-4}\cos4[/tex]

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