Lovely Heart Curve!

Calculus Level 3

Image Credit: Penguin Image Credit: Penguin

Mai Valentine and Joey Wheeler continued to decide what to decorate for the party. Instead of copying the graph above formed by the following parametric equations x(t)=16sin3(t)y(t)=13cos(t)5cos(2t)2cos(3t)cos(4t) \begin{array}{rl} x(t) &= 16\sin^3(t)\\ y(t) &= 13\cos(t) - 5\cos(2t) - 2\cos(3t) - \cos(4t) \end{array}

they thought that creating the wave related to the heart curve, similar to the following example:

Image Credit: Wikipedia Image Credit: Wikipedia

However, since some of their friends dislike jump discontinuities, they were concerned that

For all real tt, the wave graph of the parametric equations contains at least a jump discontinuity.

Does there exist a jump discontinuity of the wave graph, or were Joey and Mai imagining?


This is the end of third chapter of the story. Check out the following chapters:

First - Second - Third - Fourth - Fifth

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