lim    sen(xy+2y²)/(3xy+6y²)

(x,y)-->(0,0)

lim    sen(xy+2y²)/3(xy+2y²)

(x,y)-->(0,0)

lim    (1/3) * sen(xy+2y²)/3(xy+2y²)

(x,y)-->(0,0)

lim    (1/3)    *  lim    sen(xy+2y²)/(xy+2y²)

(x,y)-->(0,0)              (x,y)-->(0,0)

lim    (1/3)    *   1   = 1/3  é a resposta  

(x,y)-->(0,0)            

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Observe: Limite fundamental

Lim    (sen x) /x =1

x-->0

lim    sen(xy+2y²)/(xy+2y²)

(x,y)-->(0,0)  

fazendo z=xy+2y²  ; (x,y)-->0 ==> z -->0

lim    (sen z) /z  = 1

z-->0