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This is an experiment to demonstrate logistic differential equations... Haha.

\[ \large \int_0^\pi \frac {dx}{(\sqrt{17} - \cos(x) )^3} \]

If the integral above equals to \( \frac {a \pi}{b} \) for coprime positive integers \(a\) and \(b\), calculate \(a+b\).

\[\large \lim_{x \to 0} \frac{2017 - \sum_{k=1}^{2017} \cos kx}{x^2} \]

The above limit can be expressed in the form \( \dfrac{4035a(a+1)}{b} \), where ...

A horizontal plank of mass \(m\) and length \(L\) is pivoted at one end and is attached by a spring of force constant \(k\) at the other end.

A small ...

The ant, located on a vertex of a cube, wishes to reach the wheat at the opposite vertex of the cube. The ant selects an adjacent edge uniformly at random ...

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