Question

Examine the continuity of f : R2 → R at (0; 0), where for all (x; y) ∈ R2,
1.)f(x; y) :=
{xy cos(1/x) if x ̸= 0;
0 if x = 0:}

2.)f(x; y) :=
{1 if x > 0 & 0 < y < x2;
0 otherwise:}

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