MathDB

1

Part of 2009 IMC

Problems(2)

IMC 2009 Day 1 P1

Source:

7/14/2014
Suppose that f,g:R→Rf,g:\mathbb{R}\to \mathbb{R} satisfying f(r)\le g(r)  \forall r\in \mathbb{Q} Does this imply f(x)\le g(x)  \forall x\in \mathbb{R} if
(a)ff and gg are non-decreasing ? (b)ff and gg are continuous?
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IMC 2009 Day 2 P1

Source:

7/15/2014
Let ℓ\ell be a line and PP be a point in R3\mathbb{R}^3. Let SS be the set of points XX such that the distance from XX to ℓ\ell is greater than or equal to two times the distance from XX to PP. If the distance from PP to ℓ\ell is d>0d>0, find Volume(S)\text{Volume}(S).
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