Solve the inequality

.

Solve the inequality

for .

Calculate the limit

Given a triangle with height , where the interior angles opposite the height measure and . Determine the ratio of the area of the triangle to its perimeter with respect to .

Prove that if the area of the circle circumscribed about a right triangle is times greater than the area of the triangle, then the triangle is isosceles.

Find all for which the equation

holds. In the answer, give the first three digits of the decimal expansion of the obtained solution, ignoring the decimal point.

The number 

The set of the solutions of the inequality   is of the form:

Let and .

A derivative of the function at equals

The value of the expression

for certain values of and is