[/quote]
,
be a parallelogram of center 
.
,
and 
such that 
.
Compute -![\begin{align*}
\frac{\mathrm{d}}{\mathrm{d}x} \bigg[ \int_{0}^{e^x} \log ( t ) \cos^4 ( t ) \mathrm{d}t \bigg]
\end{align*}](http://latex.artofproblemsolving.com/8/6/f/86fb48db976012106bd30f74cb6ada8c6e6d7800.png)
For 
define 
Determine the open interval(s) (if any) where 
is decreasing and all the open interval(s) (if any) where 
Determine all the local minima of 
.
lies on 
such that 
.
passing trough 
at 
.
.
of positive integers such that
,
.
and 
Prove that
with circumcenter 
,
be an arbitrary point on the circumcircle of triangle 
and that line 
is not parallel to line 
.
be the point on the circumcircle of triangle 
is perpendicular to 
be the point on line 
.
be the points on the circumcircle of triangle 
is a diameter, and 
and 
are parallel. Let 
be the midpoint of 
.
and 
are perpendicular.
and 
are perpendicular.
be nonnegative real numbers such that 
.
are natural numbers satisfy that: 
and 
are prime numbers. Prove that 
is a perfect squared number
Prove that
Y by
Paca-Vaca decided to note every day a single quadratic polynomial of the form 
, where 
and 
are positive integers, less or equal than 
. He follows the rule that the polynomial he writes must not have any common roots with the polynomials previously noted.
What is the maximum amount of days Paca-Vaca can follow this plan?
, where 
and 
are positive integers, less or equal than 
. He follows the rule that the polynomial he writes must not have any common roots with the polynomials previously noted.What is the maximum amount of days Paca-Vaca can follow this plan?
