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) $\frac { m ^ { 2 } } { 1 + m ^ { 2 } }$

Question

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) $\frac { m ^ { 2 } } { 1 + m ^ { 2 } }$

Quizplus · Accepted Answer

The Answer of 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) $\frac { m ^ { 2 } } { 1 + m ^ { 2 } }$

Let f(x,y)=xyx2+y2f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }f(x,y)=x2+y2xy​

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