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xy = cos (x + y) and other implicit equations that are surprisingly easy to plot

Published online by Cambridge University Press:  15 February 2024

Michael Jewess*
The Long Barn, Townsend, Harwell, Oxfordshire OX11 0DX e-mail:


The following equations relate y only implicitly to x:(1)(2) In both equations, y is a function of x for a continuous range of (x, y) values in the real x-y plane. (1) represents an ellipse. (2) has been designed by the author to have a solution in the real x-y plane at (−1, 2), and because the function on the left-hand side of (2) meets certain conditions regarding continuity and partial differentiability there must be a line of points in the real x-y plane satisfying (2) and passing continuously through (−1, 2) [1, pp. 23-28].

© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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