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Broad Topics > Pre-Calculus and Calculus > Differentiation of parametric and implicit functions

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Squareness

Age 16 to 18 Challenge Level:

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

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Folium of Descartes

Age 16 to 18 Challenge Level:

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

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Implicitly

Age 16 to 18 Challenge Level:

Can you find the maximum value of the curve defined by this expression?