If f(x,y)=y/x does limit f(x, y) exists? Justify

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Suresh Chand · Accepted Answer

Solution: Here (f(x, y) = frac{y}{x}) As (x, y) → (0, 0), we get f(x, y) → (frac{0}{0}) form So, set y = mx for x ≠ 0 where m is some constant value then, (f(x, y) = frac{mx}{x} = m) Along y → 0, we observe m → 0 and we get (lim_{(x, y) to (0, 0)} f(x, y) = 0) along y = mx And at m = 1, (lim_{(x, y) to (0, 0)} f(x, y) = 1)    k = 1 Thus (lim_{(x, y) to (0, 0)} f(x, y) enspace along enspace y = mx neq lim_{(x, y) to (0, 0)} f(x, y) enspace k = 1) So, the limit doesn't exist.

If f(x, y) = \(\frac{y}{x}\) does \(\lim_{(x,y) \to (0, 0)} f(x, y)\) exists? Justify

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If f(x, y) = \(\frac{y}{x}\) does \(\lim_{(x,y) \to (0, 0)} f(x, y)\) exists? Justify

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