Question

2xy/3x+y What is answer when x limit zero & y limit zero ?????

Answer 1

\[\lim_{x,y \to 0}\frac{2xy}{3x+y}\]
divide by xy
you get
\[\lim_{x,y \to 0}\frac{2}{\frac{3}{y}+\frac{1}{x}}\]

Answer 2

we can now evaluate
\[\lim_{y \to 0}\frac{3}{y}=\infty\] and
\[\lim_{x \to 0}\frac{1}{y}=\infty\]
hence we have
\[\lim_{x,y \to 0}\frac{2xy}{3x+y}=\frac{2}{\infty}=0\]

Answer 3

thank u .....is it indeterminate form???

Answer 4

@hartnn

Answer 5

yes, jonask ?

Answer 6

underterminate shud mean that we cant decide about the limit right
for example
\[\infty^\infty\]
but here we know the limit is 0

Answer 7

so its derterminate

Answer 8

thanks lot

Answer 9

and hey, lahiru,
\(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)

Answer 10

\[\Huge \color{purple} { WELCOME ,LAHIRU} !!!\]

Answer 11

what if you come along the path \[y=-\sin(3x)\]

Answer 12

\[y=-3\sin(x)\] is a little nicer.

Answer 13

Just to be clear...I'm saying the limit does not exist.