Метод промежутков mavzusidan test savollari

Tengsizlikni yeching.

(x-2)(x+3)>0

Ushbu (y+6)(y+2)<0 tengsizlikning barcha butun yechimlari yig‘indisini toping.

Tengsizlikni yeching.

(x-1)(x+2)>0

Tengsizlikni yeching.

(x+2)(x-3)>0

Tengsizlikning manfiy butun yechimlari yig‘indisini toping.

\frac{(x-5)(x+3)}{(x+1)^{2}}\le 0

Tengsizlikni yeching.

\frac{x-1}{x-2}\ge 0

Tengsizlikni yeching.

\frac{(x+2)(x-1)}{x+3}\le 0

Tengsizlikning eng katta va eng kichik butun yechimlari ayirmasini toping.

\frac{(x-4)(x+2)}{(x-1)^{2}}<0

Tengsizlikni yeching.

\frac{x-2}{x-1}\le 0

Tengsizlikni yeching.

\frac{(x+3)(x-5)}{x+1}\ge 0

Tengsizlikning eng katta va eng kichik butun yechimlari yig‘indisini toping.

\frac{(x+4)(3-x)}{(x-2)^{2}}>0

Tengsizliklar sistemasining butun yechimlari yig‘indisini toping.

\begin{cases}\frac{(x+4)(x-5)}{(x-1)^{2}}\le 0 \\x\ge -6 \end{cases}

Quyidagi tengsizliklardan qaysilari o‘zaro teng kuchli?

1) \frac{x-3}{x+1}\ge 0;

2) \frac{x-3}{x^{2}+1}\ge 0;

3) \frac{x-3}{x^{2}}\ge 0;

4) x-3\ge 0;

Tengsizlikning barcha butun yechimlari yig‘indisini toping.

(x-1)(x+1)^{2}(x-3)^{3}(x-4)^{4}\le 0

Ushbu (x+3)(x-2)^{2}(x+1)^{3}(x-5)^{4}\le 0 tengsizlikning barcha butun yechimlari yig‘indisini toping.

Tengsizlikni yeching.

\frac{x+1}{x-2}\le 0

Ushbu \frac{x-4}{2x+6}\le 0 tengsizlikning barcha butun sonlardagi yechimlari yig‘indisini toping.

x ning \frac{x+5}{(x+6)^{2}}<0 tengsizlikni qanoatlantiruvchi eng katta butun qiymatini toping.

\frac{x^{2}(x-1)}{x+3}\ge 0 tengsizlikni yeching.

\frac{x(x-1)^{2}}{(x+2)^{3}}\le 0 tengsizlikni yeching.

Funksiyaning aniqlanish sohasini toping.

y=\sqrt{\frac{x^{2}-4x+4}{1-x^{2}}}

Funksiyaning aniqlanish sohasini toping.

y=\frac{\sqrt{x^{2}-3x+2}+\sqrt{x}}{\sqrt{3-x}}

Ushbu y=\sqrt{\frac{(x-1)(3-x)}{x(4-x)}} funksiyaning aniqlanish sohasini toping.

Funksiyaning aniqlanish sohasini toping.

y=\sqrt{\frac{(x-2)(5-x)}{(x-3)(x-4)}}

Ushbu \sqrt{\frac{(x-2)(4-x)}{x(x+1)}} funksiyaning aniqlanish sohasini toping.

Funksiyaning aniqlanish sohasini toping.

y=\sqrt{x^{2}-9}+\frac{2}{\sqrt{-x}}

Ushbu y=\sqrt{3x-x^{3}} funksiyaning aniqlanish sohasini toping.

Ushbu \frac{x^{2}-4x+3}{x^{2}-7x+10}\le 0 tengsizlikning butun musbat yechimlari yig‘indisini toping.

Ushbu x^{5}-16x>0 tengsizlikning eng kichik butun musbat va eng katta butun manfiy yechimlari ko‘paytmasini toping.

Tengsizlikning butun musbat yechimlari nechta?

\frac{(-x^{2}+x-1)(x^{2}+x-2)}{x^{2}-7x+12}\ge 0