In this problem set we present four questions:
(Middle School Students)
The irrational number is formed
by using alternating blocks of and zeros, where the th block
of zeros following the decimal contains zeros. What is the digit
in the 2550th place following the decimal?
(High School Students) Consider the function given by
Find the maximum and minimum value of the function.
(Undergraduate Students) Let be an infinitely differentiable function, such that
- and where and is the -th derivative of
Let is given by
Decide whether is infinitely differentiable on .
(Masters Students and above) If is a measurable subset of such that
then has measure