Question

answer this question

Answer 1

\[\lim_{(x,y) \rightarrow(0,0)} x ^{2}-2 \div 3+y^{2}\] is the answer 0 ?

Answer 2

is it
\[x ^{2}-\frac{ 2 }{ 3 }+y ^{2}\]

Answer 3

nope its (x^2-2)/(3+y^2)

Answer 4

all you have to do is distribute the limits, for a constant... the limit cannot affect the constant, it's equal to the constant.... terms with variables x and y will only be affected...

Answer 5

\[\lim_{(x,y) \rightarrow (0,0)}\frac{ (x^{2}-2) }{ (3+y^{2}) }=\frac{\lim_{(x,y) \rightarrow (0,0)}x^{2}-\lim_{(x,y) \rightarrow (0,0)}2}{\lim_{(x,y) \rightarrow (0,0)}3+\lim_{(x,y) \rightarrow (0,0)}y^{2}}=\frac{ (0-2) }{ (3+0) }=-\frac{ 2 }{ 3 }\]
this is the answer... :)