Let eps be a real number greater than zero. Calculate the limit lim(x-->oo)[x^(1-eps)*Integral(from x to x+1) sin(t^2)dt] .

The square grid is given in the Euclidean plane. All grid points therefore have integer coordinates. Investigate whether there are three points in this grid plane that form an equilateral triangle.

A regular polygon with n sides of length 1 is drawn. Then, the n midpoints of the edges are used to create another regular polygon inside the first. What is the length of an edge of the new polygon? As n approaches infinity, what does this length approach?

Hopefully this task is suitable for Maple?

Inspired by the task "With two cuts into 4 equal areas" I remember the following old task:

How can you divide a cube into 6 pyramids so that their volumes are 1 : 2 : 3 : 4 : 5 : 6?

We are looking for all triangles (with the exception of similarity) in which the tangent values ​​of the interior angles are all integers.