Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.2 Partial Derivatives, #50 · Multivariable Calculus · Partial derivatives

Show that … along every straight line … to the origin

This problem is about limits in two dimensions.

Show that $x^{2} y / (x^{4} + y^{2}) \to 0$ along every straight line $y = m x$ to the origin. But traveling down the parabola $y = x^{2}$ , the ratio equals $______$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.2 Partial Derivatives, #50

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