Let $f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }$

question 100

Multiple Choice

Let $f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }$ and let $C _ { m }$ be the curve with the equation $y = m x$ , where $m$ is a constant. The value of the limit of $F ( x , y )$ as $( x , y )$ approaches $( 0,0 )$ along $C _ { m }$ is

• A)0
• B) \(\frac { 1 } { 2 }\)
• C)1
• D) \(\frac { m } { 1 + m ^ { 2 } }\)
• E) \(\frac { m ^ { 2 } } { 1 + m ^ { 2 } }\)

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