Consider evaluating the limit $\lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}-y^{2}}{7 x^{2}+3 y^{2}}$ (a) Evaluate the limit along the path $C _ { 1 } : y = 0$ (b) Evaluate the limit along the path $C _ { 2 } : x = 0$ (c) What can you conclude about the existence of $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { x ^ { 2 } - y ^ { 2 } } { 7 x ^ { 2 } + 3 y ^ { 2 } }$ ?

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The Answer of Consider evaluating the limit $\lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}-y^{2}}{7 x^{2}+3 y^{2}}$ (a) Evaluate the limit along the path $C _ { 1 } : y = 0$ (b) Evaluate the limit along the path $C _ { 2 } : x = 0$ (c) What can you conclude about the existence of $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { x ^ { 2 } - y ^ { 2 } } { 7 x ^ { 2 } + 3 y ^ { 2 } }$ ?

Consider Evaluating the Limit lim⁡(x,y)→(0,0)x2−y27x2+3y2\lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}-y^{2}}{7 x^{2}+3 y^{2}}lim(x,y)→(0,0)​7x2+3y2x2−y2​

Consider Evaluating the Limit $\lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}-y^{2}}{7 x^{2}+3 y^{2}}$