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Найдите обьединение числовых промежутков. \[ (1,3 ; 10) \text { и }(-2 ; 11) \]

Ask by Malone George. in Kazakhstan
Oct 29,2024

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Объединение числовых промежутков \( (1, 3) \) и \( (-2, 11) \) будет \( (-2, 11) \).

Solución

Чтобы найти объединение числовых промежутков \( (1, 3) \) и \( (-2, 11) \), нужно определить, какие значения входят в оба промежутка. 1. Промежуток \( (1, 3) \) включает все числа, которые больше 1 и меньше 3. 2. Промежуток \( (-2, 11) \) включает все числа, которые больше -2 и меньше 11. Теперь найдем объединение этих двух промежутков: - Начало объединения: минимальное значение из двух промежутков — это -2 (из \( (-2, 11) \)). - Конец объединения: максимальное значение — это 11 (из \( (-2, 11) \)). Таким образом, объединение промежутков будет: \[ (-2, 11) \] Промежуток \( (1, 3) \) полностью входит в \( (-2, 11) \), поэтому объединение остается \( (-2, 11) \).

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