Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.2 Partial Derivatives, #52 · Multivariable Calculus · Partial derivatives

Which functions approach zero as … and why

This problem is about limits in two dimensions.

Which functions approach zero as $(x, y) \to (0, 0)$ and why?
(a) $\frac{x y ^{2}}{x ^{2} + y ^{2}}$ (b) $\frac{x ^{2} y ^{2}}{x ^{4} + y ^{4}}$ (c) $\frac{x ^{m} y ^{n}}{x ^{m} + y ^{n}}$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.2 Partial Derivatives, #52

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