be an isosceles triangle with 
.
,
and 
,
.
is tangent to 
.
,
.
such that for any 
:
,
units horizontally (left or right); or
and 
,
to 
using at most 
moves.
such that 
for all positive integers 
.
and 
,
,
,
and 
respectively, and the points 
are collinear.
where 
is the inverse gamma function, and 
is the inverse of 
is a polynomial with integer coefficients, with 
odd. Suppose that 
for all 
Prove that 
is nonzero for all 
,
Prove that 
.
converges then so does 
for integers,
= 
= 
, as 
the 
which gets us the 
form therefore L'hopital came to my mind , which might be a completely wrong intuition, anyway what should i do to find that limit
![\[I=\int\limits_{-\infty}^{\infty}e^{x-10\cosh (2x)}\mathrm dx.\]](http://latex.artofproblemsolving.com/5/b/6/5b61a79360c164fcd935eb613e12ab056847a93c.png)
Y by Adventure10, Mango247
On the sides 
and 
of a rhombus 
we consider the points 
and 
respectively. The line 
intersects the segment 
in the point 
, and the line 
intersects the segment in the point 
. We denote by 
the intersection between the line 
and the side 
and with 
the intersection point between the line 
and the side 
.
Prove that the triangles
and 
have the same area.
and 
of a rhombus 
we consider the points 
and 
respectively. The line 
intersects the segment 
in the point 
, and the line 
intersects the segment in the point 
. We denote by 
the intersection between the line 
and the side 
and with 
the intersection point between the line 
and the side 
.Prove that the triangles
and 
have the same area.This post has been edited 1 time. Last edited by Valentin Vornicu, Apr 2, 2005, 2:09 PM
have the same altitudes from the vertices 
to the sides 
,
.
,
be the side of the square and 
,
,
.
regardless of 
.
,
.
,
.
,
.
,
.
.
or 
