Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.2 Partial Derivatives, #45 · Multivariable Calculus · Partial derivatives

Complete these four correct definitions of limit

This problem is about limits in two dimensions.

Complete these four correct definitions of limit. 1 The points $(x_{n}, y_{n})$ approach the point $(a, b)$ if $x_{n}$ converges to $a$ and $______$ . 2 For any circle around $(a, b)$ , the points $(x_{n}, y_{n})$ eventually go $______$ the circle and stay $______$ . 3 The distance from $(x_{n}, y_{n})$ to $(a, b)$ is $______$ and it approaches $______$ . 4 For any $ε > 0$ there is an $N$ such that the distance $______< ε$ for all $n > N$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.2 Partial Derivatives, #45

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