Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.2 Partial Derivatives, #46 · Multivariable Calculus · Partial derivatives

Find … and … and the limit … if it exists

This problem is about limits in two dimensions.

Find $(x_{2}, y_{2})$ and $(x_{4}, y_{4})$ and the limit $(a, b)$ if it exists. Start from $(x_{0}, y_{0}) = (1, 0)$ .
(a) $(x_{n}, y_{n}) = (1/ (n + 1), n / (n + 1))$
(b) $(x_{n}, y_{n}) = (x_{n - 1}, y_{n - 1})$
(c) $(x_{n}, y_{n}) = (y_{n - 1}, x_{n - 1})$
(d) $(x_{n}, y_{n}) = (x_{n - 1} + y_{n - 1}, x_{n - 1} - y_{n - 1})$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.2 Partial Derivatives, #46

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