Question

O limite (x,y) =>(2,4) ( x + 4) / ( x²y - 3y +4x² -12) , vale :

a) 1
b) -1
c) 0
d) -8
e) 12

Answer 1

Boa tarde Roger!

Para resolver esse limite,basta substituir os valores,pois o mesmo não apresenta indeterminação é só fazer a substituição.


$\displaystyle \lim_{(x,y) \to (2,4)} \frac{y+4}{ x^{2} y-3y+4 x^{2} -12} \\\\\\\\\\\ \displaystyle \lim_{(x,y) \to (2,4)} \frac{4+4}{ (2)^{2} .4-3(4)+4.(2)^{2} -12} \\\\\\\\\\\ \displaystyle \lim_{(x,y) \to (2,4)} \frac{4+4}{ 4.4-3(4)+4.(4) -12} \\\\\\\\\\\ \displaystyle \lim_{(x,y) \to (2,4)} \frac{4+4}{ 16-12+16 -12} \\\\\\\\\\\ \displaystyle \lim_{(x,y) \to (2,4)} \frac{8}{ 32-24} \\\\\\\\\\\ \displaystyle \lim_{(x,y) \to (2,4)} \frac{8}{8}$


$\displaystyle \lim_{(x,y) \to (2,4)} 1\\\\\\\\\\\\ \boxed{Resposta:~~Alternativa~~A}$

Boa tarde!

Bons estudos!

Answer 2

Resposta: 1

Explicação passo a passo:

1