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Why does the implicit equation: x^{2}+y^{2}-1)^{3}-x^{2}y^{3}=0 have an undefined slope at the point (1,0)? If you look at the graph of it, it's a cardioid (a famous one - it was used recently on a book cover) and at the point (1,0) it is neither a cusp, nor discontinuous. It LOOKS like it should just be a positive slope of approximately 1. But when I plug (1,0) into the derivative of the equation, I get 0/0. Why is this happening?
Why does the implicit equation: x^{2}+y^{2}-1)^{3}-x^{2}y^{3}=0 have an undefined slope at the point (1,0)? If you look at the graph of it, it's a cardioid (a famous one - it was used recently on a book cover) and at the point (1,0) it is neither a cusp, nor discontinuous. It LOOKS like it should just be a positive slope of approximately 1. But when I plug (1,0) into the derivative of the equation, I get 0/0. Why is this happening?
