Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.2 Partial Derivatives, #51 · Multivariable Calculus · Partial derivatives

Can you define … so that … is continuous at

This problem is about limits in two dimensions.

Can you define $f (0, 0)$ so that $f (x, y)$ is continuous at $(0, 0)$ ?
(a) $f = ∣ x ∣ + ∣ y - 1∣$ (b) $f = (1 + x)^{y}$ (c) $f = x^{1 + y}$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.2 Partial Derivatives, #51

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