✏️ Разбор задачи с экзамена ШАД
Условие: Непрерывная функция f(x) такова, что f(0)=f(2). Докажите, что для какого-то x ∈ [0,2] имеет место равенство f(x) = f(x-1).
Решение: Рассмотрим функцию
φ(1) = f(1) - f(0)
φ(2) = f(2) - f(1)
В силу равенства $f(0)=f(2)$ из условия, получим φ(1)=-φ(2). Функция φ(x) непрерывна на отрезке [1, 2], тогда по теореме Больцано-Коши о промежуточном значении найдется
Ответ:
Proglib Academy #буст
BY Proglib.academy | IT-курсы
Telegram is riding high, adding tens of million of users this year. Now the bill is coming due.Telegram is one of the few significant social-media challengers to Facebook Inc., FB -1.90% on a trajectory toward one billion users active each month by the end of 2022, up from roughly 550 million today.
The SSE was the first modern stock exchange to open in China, with trading commencing in 1990. It has now grown to become the largest stock exchange in Asia and the third-largest in the world by market capitalization, which stood at RMB 50.6 trillion (US$7.8 trillion) as of September 2021. Stocks (both A-shares and B-shares), bonds, funds, and derivatives are traded on the exchange. The SEE has two trading boards, the Main Board and the Science and Technology Innovation Board, the latter more commonly known as the STAR Market. The Main Board mainly hosts large, well-established Chinese companies and lists both A-shares and B-shares.
Proglib academy | IT курсы from ye