11.1

Part of III Soros Olympiad 1996 - 97 (Russia)

Problems(3)

{ tg x } = sinx (III Soros Olympiad 1996-97 R1 11.1)

Source:

Find the smallest positive root of the equation

\{tg x\}=\sin x.

\{a\}

is the fractional part of

a

\{a\}

is equal to the difference between

a

and the largest integer not exceeding

a

trigonometryalgebrafractional part

sum of consecutive numbers (III Soros Olympiad 1996-97 R2 11.1)

Source:

The sum of several consecutive natural numbers is

20

times greater than the largest of them and

30

times greater than the smallest. Find these numbers.

x2^(1/x)+1/x 2^x=4 (III Soros Olympiad 1996-97 R3 11.1)

Source:

Solve the equation:

x \cdot 2^{\dfrac{1}{x}}+\dfrac{1}{x} \cdot 2^x=4