Know your limits

Calculus Level 2

$\lim _{ \left( x,y \right) \rightarrow \left( 1,1 \right) }{ \frac { { x }^{ 2 }y-{ y }^{ 2 }x }{ \sqrt { x } -\sqrt { y } } \quad =\quad ? }$

Note: Enter 999 if the limit does not exist or is not defined.

The answer is 2.

1 solution

Zeeshan Ali
Jan 23, 2016

$\lim _{ \left( x,y \right) \rightarrow \left( 1,1 \right) }{ \frac { { x }^{ 2 }y-{ y }^{ 2 }x }{ \sqrt { x } -\sqrt { y } } \quad =\quad } \lim _{ \left( x,y \right) \rightarrow \left( 1,1 \right) }{ \frac { { x }y(x-y) }{ \sqrt { x } -\sqrt { y } } \quad =\quad } \lim _{ \left( x,y \right) \rightarrow \left( 1,1 \right) }{ \frac { { x }y(\sqrt { x } -\sqrt { y } )(\sqrt { x } +\sqrt { y } ) }{ \sqrt { x } -\sqrt { y } } \quad =\quad } \lim _{ \left( x,y \right) \rightarrow \left( 1,1 \right) }{ { \quad x }y(\sqrt { x } +\sqrt { y } )\quad =\quad 1\times 1\times (\sqrt { 1 } +\sqrt { 1 } ) } \quad =\quad \boxed{02}$

Should not (x,y) $\rightarrow$ (1,1).

Rishabh Jain - 5 years, 4 months ago

Oops! Well... I've mistaken it as (0,0). Thanks.. I have edited the problem now

Zeeshan Ali - 5 years, 4 months ago

Well it has cost me good 100 points.. :D ......BTW no problem..

Rishabh Jain - 5 years, 4 months ago

@Rishabh Jain – Thanks. Those who answered 0 have been marked correct.

In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the “dot dot dot” menu in the lower right corner. This will notify the problem creator who can fix the issues.

Calvin Lin Staff - 5 years, 4 months ago

Know your limits

The answer is 2.

1 solution

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