Using the Fact That $\left| \frac { y ^ { 2 } ( x - 2 ) } { ( x - 2 ) ^ { 2 } + y ^ { 2 } } \right| \leq \sqrt { ( x - 2 ) ^ { 2 } + y ^ { 2 } }$

question 14

Essay

Using the fact that $\left| \frac { y ^ { 2 } ( x - 2 ) } { ( x - 2 ) ^ { 2 } + y ^ { 2 } } \right| \leq \sqrt { ( x - 2 ) ^ { 2 } + y ^ { 2 } }$ for all x and y except $( x , y ) = ( 2,0 )$ ,
show that $\lim _ { ( x , y ) \rightarrow ( 2 \rho ) } \frac { y ^ { 2 } ( x - 2 ) } { ( x - 2 ) ^ { 2 } + y ^ { 2 } } = 0$ .

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