MathDB

11.2

Part of VI Soros Olympiad 1999 - 2000 (Russia)

Problems(3)

f''(0) , (...((x - 2)^2 - 2)^2 - 2)^2..- VI Soros Olympiad 1999-00 Round 1 11.2

Source:

5/21/2024
Let f(x)=(...((x−2)2−2)2−2)2...−2)2f(x) = (...((x - 2)^2 - 2)^2 - 2)^2... - 2)^2 (here there are nn brackets ()( )). Find f′′(0)f''(0)
algebraderivativecalculus
bus, cyclist, motorcyclist, pedestrian (VI Soros Olympiad 1990-00 R2 11.2)

Source:

5/28/2024
A bus and a cyclist left town AA at 1010 o'clock in the same direction, and a motorcyclist left town BB to meet them 1515 minutes later. The bus drove past the pedestrian at 1010 o'clock 3030 minutes, met the motorcyclist at 1111 o'clock and arrived in the city of BB at 1212 o'clock. The motorcyclist met the cyclist 1515 minutes after meeting the bus and another 1515 minutes later caught up with the pedestrian. At what time did the cyclist and the pedestrian meet? (The speeds and directions of movement of all participants were equal, the pedestrian and the motorcyclist were moving in the direction of city AA.)
algebra
sum of all products of k_1k_2...k_{999} (VI Soros Olympiad 1990-00 R3 11.2)

Source:

5/28/2024
Find the sum of all possible products of natural numbers of the form k1k2...k999k_1k_2...k_{999}, where in each product k1<k2<...<k999<1999 k_1 < k_2 < ... < k_{999} <1999, and there are no kik_i and kjk_j such that ki+kj=1999k_i + k_j =1999.
algebranumber theory