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

Short Answer

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