MathDB

Problem 8

Part of 2019 LIMIT Category B

Problems(2)

increasing/decreasing function

Source: LIMIT 2019 CBS1 P8

4/28/2021
If f(x)=cos⁡(x)−1+x22f(x)=\cos(x)-1+\frac{x^2}2, then <spanclass=′latex−bold′>(A)</span> f(x) is an increasing function on the real line<span class='latex-bold'>(A)</span>~f(x)\text{ is an increasing function on the real line} <spanclass=′latex−bold′>(B)</span> f(x) is a decreasing function on the real line<span class='latex-bold'>(B)</span>~f(x)\text{ is a decreasing function on the real line} <spanclass=′latex−bold′>(C)</span> f(x) is increasing on −∞<x≤0 and decreasing on 0≤x<∞<span class='latex-bold'>(C)</span>~f(x)\text{ is increasing on }-\infty<x\le0\text{ and decreasing on }0\le x<\infty <spanclass=′latex−bold′>(D)</span> f(x) is decreasing on −∞<x≤0 and increasing on 0≤x<∞<span class='latex-bold'>(D)</span>~f(x)\text{ is decreasing on }-\infty<x\le0\text{ and increasing on }0\le x<\infty
function
polygon with prime # of sides

Source: LIMIT 2019 CBS2 P8

4/28/2021
Given a regular polygon with pp sides, where pp is a prime number. After rotating this polygon about its center by an integer number of degrees it coincides with itself. What is the maximal possible number for pp?
geometrynumber theory