Use the two-path test to prove that the following limit does not exist. [ lim _{(x, y) ightarrow(0,0)} frac{y^{4}-2 x^{2}}{y^{4}+x^{2}} ] What value does ( f(x, y)=frac{y^{4}-2 x^{2}}{y^{4}+x^{2}} ) approach as ( (x, y) ) approaches ( (0,0) ) along the ( x )-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. ( f(x, y) ) approaches ( square ). (Simplify your answer.) B. ( f(x, y) ) approaches ( -infty ). C. ( f(x, y) ) approaches ( infty ). D. ( f(x, y) ) has no limit as ( (x, y) ) approaches ( (0,0) ) along the ( x )-axis.
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The two-path test states that if we can find two paths along a point such that if we evaluate the limit, it will give different values, then the limit does not exist at that point. ** Show more…
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