## AMS Undergraduate Mathematics Contest: #2

Those wishing to submit solutions should see submission instructions for details. Submission Deadline: February 18th, 2013

Compute the following limit or explain why it doesn’t exist: $\displaystyle \lim_{x \to 0} \frac{x^{2} \sin\left(\frac{1}{x}\right)}{\sin\left(x\right)}$.

Two eligible contestants will be selected for $15 gift-certificates to Woody’s of Golden. One recipient will be randomly selected from correct responses submitted by eligible contestants. A second$15 gift-certificate will be awarded to the most elegant solution as chosen by the AMS Outreach Committee.

## The Heap

If there are no prizes awarded for a given contest question then we will move it to the heap for general submissions. Please see submission instructions for more information.

Old questions on the heap, whose prizes were not awarded, will be open additional submissions from anyone. After 50 submissions is reached we will randomly select a correct submission for a prize. In this case any submission is eligible for a prize.

## AMS Undergraduate Mathematics Contest: #1

Those wishing to submit solutions should see submission instructions for details. Submission Deadline: January 30th, 2013

Given the following triangle,

and assuming the exterior angle at $A$ is fixed at $120^{\circ}$ and that the length
of $AB$ is fixed at $1$, find $\displaystyle \lim_{\theta \to 0} (r-s)$.

Two eligible contestants will be selected for $15 gift-certificates to Woody’s of Golden. One recipient will be randomly selected from correct responses submitted by eligible contestants. A second$15 gift-certificate will be awarded to the most elegant solution as chosen by the AMS Outreach Committee.

## Welcome Back!

Treegonometry solves Christmas decoration dilemma

Treegonometry in action!

Apparently researchers at the University of Sheffield had a problem with decorating their tree so that it was neither too barren nor too gaudy. Thus, we now have a mathematical formula to define the number of baubles, the height of the angel on top, the length of tinsel, and, of course, the length of tree lights to use. If you’re curious, the length of lights is π x (height of the tree).