Find the Limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { \sin \left( 9 x ^ { 2 } + 9 y ^ { 2 } \right) } { 7 x ^ { 2 } + 7 y ^ { 2 } }$

Find the limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { \sin \left( 9 x ^ { 2 } + 9 y ^ { 2 } \right) } { 7 x ^ { 2 } + 7 y ^ { 2 } }$ Hint: If $x = r \cos \theta$ and $y = r \sin \theta ,$ then $( x , y ) \rightarrow ( 0,0 )$ if and only if $r \rightarrow 0 ^ { + }$

A) $\frac { 9 } { 7 }$
B) $1$
C) $0$
D) $\frac { 7 } { 9 }$

Correct Answer:

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