11.1

Part of II Soros Olympiad 1995 - 96 (Russia)

Problems(3)

-3<=(x^2+ax+b)/(x^2-x+1)<=2 (II Soros Olympiad 1995-96 R1 11.1)

Source:

a

b

for which the largest and smallest is values of the function

y=\frac{x^2+ax+b}{x^2-x+1}

are equal to the

2

-3

algebrainequalities

antiderivative of y = 1/x^3 (II Soros Olympiad 1995-96 R2 11.1)

Source:

Find some antiderivative of the function

y = 1/x^3

, the graph of which has exactly three common points with the graph of the function

y = |x|

calculusalgebraintegrationIntegral

log_{10} (x^3+x)=log_2 x (II Soros Olympiad 1997-98 R3 11.1)

Source:

Solve the equation

\log_{10} (x^3+x)=\log_2 x.

algebralogarithms