This one I gave my students today, nobody solve it.
Is a following function periodic
If someone is interested I can show a solution later.
Without using the derivative, the equation has only one solution. Indeed, if then so there exists such that and , so . But is not rational ; absqrt.
This may be overkill, but at least the same reasoning can prove the following : given any -periodic function g with and such that for , the function is not periodic. For instance, this is also true if g is the Weierstrass function (if , with the definition used by wiki).
Let P(x, y) be the terminal point on the unit circle determined by t. Then
please provide answer for this question