MathDB

2

Part of 1986 Iran MO (2nd round)

Problems(2)

Functions f, g - [Iran Second Round 1986]

Source:

12/24/2010
(a) Sketch the diagram of the function ff if f(x)=4x(1-|x|) ,   |x| \leq 1.
(b) Does there exist derivative of ff in the point x=0 ?x=0 \ ?
(c) Let gg be a function such that g(x)={f(x)xemsp;:x≠0 4    emsp;:x=0g(x)=\left\{\begin{array}{cc}\frac{f(x)}{x}   : x \neq 0\\ \text{ } \\ 4 \ \ \ \   : x=0\end{array}\right. Is the function gg continuous in the point x=0 ?x=0 \ ?
(d) Sketch the diagram of g.g.
functioncalculusderivativelimitalgebra proposedalgebra
Find the area in terms of a, b - [Iran Second Round 1986]

Source:

12/24/2010
In a trapezoid ABCDABCD, the legs ABAB and CDCD meet in MM and the diagonals ACAC and BDBD meet in N.N. Let AC=aAC=a and BC=b.BC=b. Find the area of triangles AMDAMD and ANDAND in terms of aa and b.b.
geometrytrapezoidgeometry proposed