Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- Неравенство:
-
(x-1)/(x-5)>3
-
(x^2-4)*(x^2-9)>0
- a*x<b
-
2^x<=0
- График функции y =:
-
2^x
- Производная:
-
2^x
- Интеграл d{x}:
-
2^x
-
Идентичные выражения
- два ^x<= ноль
- 2 в степени x меньше или равно 0
- два в степени x меньше или равно ноль
- 2x<=0
- 2^x<=O
2^x<=0 неравенство
Решение
Подробное решение
Дано неравенство:
$$2^{x} \leq 0$$
Чтобы решить это нер-во - надо сначала решить соотвествующее уравнение:
$$2^{x} = 0$$
Решаем:
$$x_{1} = -54.176760093132$$
$$x_{2} = -92.176760093132$$
$$x_{3} = -96.176760093132$$
$$x_{4} = -110.176760093132$$
$$x_{5} = -82.176760093132$$
$$x_{6} = -76.176760093132$$
$$x_{7} = -100.176760093132$$
$$x_{8} = -60.176760093132$$
$$x_{9} = -124.176760093132$$
$$x_{10} = -70.176760093132$$
$$x_{11} = -86.176760093132$$
$$x_{12} = -44.176760093132$$
$$x_{13} = -74.176760093132$$
$$x_{14} = -128.176760093132$$
$$x_{15} = -52.176760093132$$
$$x_{16} = -118.176760093132$$
$$x_{17} = -116.176760093132$$
$$x_{18} = -46.176760093132$$
$$x_{19} = -114.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{21} = -56.176760093132$$
$$x_{22} = -90.176760093132$$
$$x_{23} = -88.176760093132$$
$$x_{24} = -102.176760093132$$
$$x_{25} = -40.176760093132$$
$$x_{26} = -66.176760093132$$
$$x_{27} = -48.176760093132$$
$$x_{28} = -42.176760093132$$
$$x_{29} = -72.176760093132$$
$$x_{30} = -98.176760093132$$
$$x_{31} = -122.176760093132$$
$$x_{32} = -62.176760093132$$
$$x_{33} = -50.176760093132$$
$$x_{34} = -130.176760093132$$
$$x_{35} = -68.176760093132$$
$$x_{36} = -106.176760093132$$
$$x_{37} = -94.176760093132$$
$$x_{38} = -112.176760093132$$
$$x_{39} = -108.176760093132$$
$$x_{40} = -126.176760093132$$
$$x_{41} = -84.176760093132$$
$$x_{42} = -104.176760093132$$
$$x_{43} = -78.176760093132$$
$$x_{44} = -80.176760093132$$
$$x_{45} = -64.176760093132$$
$$x_{46} = -58.176760093132$$
$$x_{1} = -54.176760093132$$
$$x_{2} = -92.176760093132$$
$$x_{3} = -96.176760093132$$
$$x_{4} = -110.176760093132$$
$$x_{5} = -82.176760093132$$
$$x_{6} = -76.176760093132$$
$$x_{7} = -100.176760093132$$
$$x_{8} = -60.176760093132$$
$$x_{9} = -124.176760093132$$
$$x_{10} = -70.176760093132$$
$$x_{11} = -86.176760093132$$
$$x_{12} = -44.176760093132$$
$$x_{13} = -74.176760093132$$
$$x_{14} = -128.176760093132$$
$$x_{15} = -52.176760093132$$
$$x_{16} = -118.176760093132$$
$$x_{17} = -116.176760093132$$
$$x_{18} = -46.176760093132$$
$$x_{19} = -114.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{21} = -56.176760093132$$
$$x_{22} = -90.176760093132$$
$$x_{23} = -88.176760093132$$
$$x_{24} = -102.176760093132$$
$$x_{25} = -40.176760093132$$
$$x_{26} = -66.176760093132$$
$$x_{27} = -48.176760093132$$
$$x_{28} = -42.176760093132$$
$$x_{29} = -72.176760093132$$
$$x_{30} = -98.176760093132$$
$$x_{31} = -122.176760093132$$
$$x_{32} = -62.176760093132$$
$$x_{33} = -50.176760093132$$
$$x_{34} = -130.176760093132$$
$$x_{35} = -68.176760093132$$
$$x_{36} = -106.176760093132$$
$$x_{37} = -94.176760093132$$
$$x_{38} = -112.176760093132$$
$$x_{39} = -108.176760093132$$
$$x_{40} = -126.176760093132$$
$$x_{41} = -84.176760093132$$
$$x_{42} = -104.176760093132$$
$$x_{43} = -78.176760093132$$
$$x_{44} = -80.176760093132$$
$$x_{45} = -64.176760093132$$
$$x_{46} = -58.176760093132$$
Данные корни
$$x_{34} = -130.176760093132$$
$$x_{14} = -128.176760093132$$
$$x_{40} = -126.176760093132$$
$$x_{9} = -124.176760093132$$
$$x_{31} = -122.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{16} = -118.176760093132$$
$$x_{17} = -116.176760093132$$
$$x_{19} = -114.176760093132$$
$$x_{38} = -112.176760093132$$
$$x_{4} = -110.176760093132$$
$$x_{39} = -108.176760093132$$
$$x_{36} = -106.176760093132$$
$$x_{42} = -104.176760093132$$
$$x_{24} = -102.176760093132$$
$$x_{7} = -100.176760093132$$
$$x_{30} = -98.176760093132$$
$$x_{3} = -96.176760093132$$
$$x_{37} = -94.176760093132$$
$$x_{2} = -92.176760093132$$
$$x_{22} = -90.176760093132$$
$$x_{23} = -88.176760093132$$
$$x_{11} = -86.176760093132$$
$$x_{41} = -84.176760093132$$
$$x_{5} = -82.176760093132$$
$$x_{44} = -80.176760093132$$
$$x_{43} = -78.176760093132$$
$$x_{6} = -76.176760093132$$
$$x_{13} = -74.176760093132$$
$$x_{29} = -72.176760093132$$
$$x_{10} = -70.176760093132$$
$$x_{35} = -68.176760093132$$
$$x_{26} = -66.176760093132$$
$$x_{45} = -64.176760093132$$
$$x_{32} = -62.176760093132$$
$$x_{8} = -60.176760093132$$
$$x_{46} = -58.176760093132$$
$$x_{21} = -56.176760093132$$
$$x_{1} = -54.176760093132$$
$$x_{15} = -52.176760093132$$
$$x_{33} = -50.176760093132$$
$$x_{27} = -48.176760093132$$
$$x_{18} = -46.176760093132$$
$$x_{12} = -44.176760093132$$
$$x_{28} = -42.176760093132$$
$$x_{25} = -40.176760093132$$
являются точками смены знака неравенства в решениях.
Сначала определимся со знаком до крайней левой точки:
$$x_{0} \leq x_{34}$$
Возьмём например точку
$$x_{0} = x_{34} - \frac{1}{10}$$
=
$$-130.176760093132 - \frac{1}{10}$$
=
$$-130.276760093132$$
подставляем в выражение
$$2^{x} \leq 0$$
$$2^{-130.276760093132} \leq 0$$
но
Тогда
$$x \leq -130.176760093132$$
не выполняется
значит одно из решений нашего неравенства будет при:
$$x \geq -130.176760093132 \wedge x \leq -128.176760093132$$
Другие решения неравенства будем получать переходом на следующий полюс
и т.д.
Ответ:
$$x \geq -130.176760093132 \wedge x \leq -128.176760093132$$
$$x \geq -126.176760093132 \wedge x \leq -124.176760093132$$
$$x \geq -122.176760093132 \wedge x \leq -120.176760093132$$
$$x \geq -118.176760093132 \wedge x \leq -116.176760093132$$
$$x \geq -114.176760093132 \wedge x \leq -112.176760093132$$
$$x \geq -110.176760093132 \wedge x \leq -108.176760093132$$
$$x \geq -106.176760093132 \wedge x \leq -104.176760093132$$
$$x \geq -102.176760093132 \wedge x \leq -100.176760093132$$
$$x \geq -98.176760093132 \wedge x \leq -96.176760093132$$
$$x \geq -94.176760093132 \wedge x \leq -92.176760093132$$
$$x \geq -90.176760093132 \wedge x \leq -88.176760093132$$
$$x \geq -86.176760093132 \wedge x \leq -84.176760093132$$
$$x \geq -82.176760093132 \wedge x \leq -80.176760093132$$
$$x \geq -78.176760093132 \wedge x \leq -76.176760093132$$
$$x \geq -74.176760093132 \wedge x \leq -72.176760093132$$
$$x \geq -70.176760093132 \wedge x \leq -68.176760093132$$
$$x \geq -66.176760093132 \wedge x \leq -64.176760093132$$
$$x \geq -62.176760093132 \wedge x \leq -60.176760093132$$
$$x \geq -58.176760093132 \wedge x \leq -56.176760093132$$
$$x \geq -54.176760093132 \wedge x \leq -52.176760093132$$
$$x \geq -50.176760093132 \wedge x \leq -48.176760093132$$
$$x \geq -46.176760093132 \wedge x \leq -44.176760093132$$
$$x \geq -42.176760093132 \wedge x \leq -40.176760093132$$
$$2^{x} \leq 0$$
Чтобы решить это нер-во - надо сначала решить соотвествующее уравнение:
$$2^{x} = 0$$
Решаем:
$$x_{1} = -54.176760093132$$
$$x_{2} = -92.176760093132$$
$$x_{3} = -96.176760093132$$
$$x_{4} = -110.176760093132$$
$$x_{5} = -82.176760093132$$
$$x_{6} = -76.176760093132$$
$$x_{7} = -100.176760093132$$
$$x_{8} = -60.176760093132$$
$$x_{9} = -124.176760093132$$
$$x_{10} = -70.176760093132$$
$$x_{11} = -86.176760093132$$
$$x_{12} = -44.176760093132$$
$$x_{13} = -74.176760093132$$
$$x_{14} = -128.176760093132$$
$$x_{15} = -52.176760093132$$
$$x_{16} = -118.176760093132$$
$$x_{17} = -116.176760093132$$
$$x_{18} = -46.176760093132$$
$$x_{19} = -114.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{21} = -56.176760093132$$
$$x_{22} = -90.176760093132$$
$$x_{23} = -88.176760093132$$
$$x_{24} = -102.176760093132$$
$$x_{25} = -40.176760093132$$
$$x_{26} = -66.176760093132$$
$$x_{27} = -48.176760093132$$
$$x_{28} = -42.176760093132$$
$$x_{29} = -72.176760093132$$
$$x_{30} = -98.176760093132$$
$$x_{31} = -122.176760093132$$
$$x_{32} = -62.176760093132$$
$$x_{33} = -50.176760093132$$
$$x_{34} = -130.176760093132$$
$$x_{35} = -68.176760093132$$
$$x_{36} = -106.176760093132$$
$$x_{37} = -94.176760093132$$
$$x_{38} = -112.176760093132$$
$$x_{39} = -108.176760093132$$
$$x_{40} = -126.176760093132$$
$$x_{41} = -84.176760093132$$
$$x_{42} = -104.176760093132$$
$$x_{43} = -78.176760093132$$
$$x_{44} = -80.176760093132$$
$$x_{45} = -64.176760093132$$
$$x_{46} = -58.176760093132$$
$$x_{1} = -54.176760093132$$
$$x_{2} = -92.176760093132$$
$$x_{3} = -96.176760093132$$
$$x_{4} = -110.176760093132$$
$$x_{5} = -82.176760093132$$
$$x_{6} = -76.176760093132$$
$$x_{7} = -100.176760093132$$
$$x_{8} = -60.176760093132$$
$$x_{9} = -124.176760093132$$
$$x_{10} = -70.176760093132$$
$$x_{11} = -86.176760093132$$
$$x_{12} = -44.176760093132$$
$$x_{13} = -74.176760093132$$
$$x_{14} = -128.176760093132$$
$$x_{15} = -52.176760093132$$
$$x_{16} = -118.176760093132$$
$$x_{17} = -116.176760093132$$
$$x_{18} = -46.176760093132$$
$$x_{19} = -114.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{21} = -56.176760093132$$
$$x_{22} = -90.176760093132$$
$$x_{23} = -88.176760093132$$
$$x_{24} = -102.176760093132$$
$$x_{25} = -40.176760093132$$
$$x_{26} = -66.176760093132$$
$$x_{27} = -48.176760093132$$
$$x_{28} = -42.176760093132$$
$$x_{29} = -72.176760093132$$
$$x_{30} = -98.176760093132$$
$$x_{31} = -122.176760093132$$
$$x_{32} = -62.176760093132$$
$$x_{33} = -50.176760093132$$
$$x_{34} = -130.176760093132$$
$$x_{35} = -68.176760093132$$
$$x_{36} = -106.176760093132$$
$$x_{37} = -94.176760093132$$
$$x_{38} = -112.176760093132$$
$$x_{39} = -108.176760093132$$
$$x_{40} = -126.176760093132$$
$$x_{41} = -84.176760093132$$
$$x_{42} = -104.176760093132$$
$$x_{43} = -78.176760093132$$
$$x_{44} = -80.176760093132$$
$$x_{45} = -64.176760093132$$
$$x_{46} = -58.176760093132$$
Данные корни
$$x_{34} = -130.176760093132$$
$$x_{14} = -128.176760093132$$
$$x_{40} = -126.176760093132$$
$$x_{9} = -124.176760093132$$
$$x_{31} = -122.176760093132$$
$$x_{20} = -120.176760093132$$
$$x_{16} = -118.176760093132$$
$$x_{17} = -116.176760093132$$
$$x_{19} = -114.176760093132$$
$$x_{38} = -112.176760093132$$
$$x_{4} = -110.176760093132$$
$$x_{39} = -108.176760093132$$
$$x_{36} = -106.176760093132$$
$$x_{42} = -104.176760093132$$
$$x_{24} = -102.176760093132$$
$$x_{7} = -100.176760093132$$
$$x_{30} = -98.176760093132$$
$$x_{3} = -96.176760093132$$
$$x_{37} = -94.176760093132$$
$$x_{2} = -92.176760093132$$
$$x_{22} = -90.176760093132$$
$$x_{23} = -88.176760093132$$
$$x_{11} = -86.176760093132$$
$$x_{41} = -84.176760093132$$
$$x_{5} = -82.176760093132$$
$$x_{44} = -80.176760093132$$
$$x_{43} = -78.176760093132$$
$$x_{6} = -76.176760093132$$
$$x_{13} = -74.176760093132$$
$$x_{29} = -72.176760093132$$
$$x_{10} = -70.176760093132$$
$$x_{35} = -68.176760093132$$
$$x_{26} = -66.176760093132$$
$$x_{45} = -64.176760093132$$
$$x_{32} = -62.176760093132$$
$$x_{8} = -60.176760093132$$
$$x_{46} = -58.176760093132$$
$$x_{21} = -56.176760093132$$
$$x_{1} = -54.176760093132$$
$$x_{15} = -52.176760093132$$
$$x_{33} = -50.176760093132$$
$$x_{27} = -48.176760093132$$
$$x_{18} = -46.176760093132$$
$$x_{12} = -44.176760093132$$
$$x_{28} = -42.176760093132$$
$$x_{25} = -40.176760093132$$
являются точками смены знака неравенства в решениях.
Сначала определимся со знаком до крайней левой точки:
$$x_{0} \leq x_{34}$$
Возьмём например точку
$$x_{0} = x_{34} - \frac{1}{10}$$
=
$$-130.176760093132 - \frac{1}{10}$$
=
$$-130.276760093132$$
подставляем в выражение
$$2^{x} \leq 0$$
$$2^{-130.276760093132} \leq 0$$
6.06439490285985e-40 <= 0
но
6.06439490285985e-40 >= 0
Тогда
$$x \leq -130.176760093132$$
не выполняется
значит одно из решений нашего неравенства будет при:
$$x \geq -130.176760093132 \wedge x \leq -128.176760093132$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x_34 x_14 x_40 x_9 x_31 x_20 x_16 x_17 x_19 x_38 x_4 x_39 x_36 x_42 x_24 x_7 x_30 x_3 x_37 x_2 x_22 x_23 x_11 x_41 x_5 x_44 x_43 x_6 x_13 x_29 x_10 x_35 x_26 x_45 x_32 x_8 x_46 x_21 x_1 x_15 x_33 x_27 x_18 x_12 x_28 x_25Другие решения неравенства будем получать переходом на следующий полюс
и т.д.
Ответ:
$$x \geq -130.176760093132 \wedge x \leq -128.176760093132$$
$$x \geq -126.176760093132 \wedge x \leq -124.176760093132$$
$$x \geq -122.176760093132 \wedge x \leq -120.176760093132$$
$$x \geq -118.176760093132 \wedge x \leq -116.176760093132$$
$$x \geq -114.176760093132 \wedge x \leq -112.176760093132$$
$$x \geq -110.176760093132 \wedge x \leq -108.176760093132$$
$$x \geq -106.176760093132 \wedge x \leq -104.176760093132$$
$$x \geq -102.176760093132 \wedge x \leq -100.176760093132$$
$$x \geq -98.176760093132 \wedge x \leq -96.176760093132$$
$$x \geq -94.176760093132 \wedge x \leq -92.176760093132$$
$$x \geq -90.176760093132 \wedge x \leq -88.176760093132$$
$$x \geq -86.176760093132 \wedge x \leq -84.176760093132$$
$$x \geq -82.176760093132 \wedge x \leq -80.176760093132$$
$$x \geq -78.176760093132 \wedge x \leq -76.176760093132$$
$$x \geq -74.176760093132 \wedge x \leq -72.176760093132$$
$$x \geq -70.176760093132 \wedge x \leq -68.176760093132$$
$$x \geq -66.176760093132 \wedge x \leq -64.176760093132$$
$$x \geq -62.176760093132 \wedge x \leq -60.176760093132$$
$$x \geq -58.176760093132 \wedge x \leq -56.176760093132$$
$$x \geq -54.176760093132 \wedge x \leq -52.176760093132$$
$$x \geq -50.176760093132 \wedge x \leq -48.176760093132$$
$$x \geq -46.176760093132 \wedge x \leq -44.176760093132$$
$$x \geq -42.176760093132 \wedge x \leq -40.176760093132$$
Решение неравенства на графике
Быстрый ответ
Данное неравенство не имеет решений
График