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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2016 • Question 9

Question

Math 6010 • Linear Models Spring 2016 • Question 9

Compute \[ \begin {aligned} \lim _{n\to \infty }(b-a)^{-n} \int _a^b\int _a^b\cdots \int _a^b \frac {x_1+x_2+\cdots +x_n}{x_1^2+x_2^2+\cdots +x_n^2} \,dx_1\,dx_2\cdots dx_n \end {aligned} \] if \(0<a<b<\infty \).

Raw LaTeX

Compute
\[
\begin{aligned}
  \lim_{n\to\infty}(b-a)^{-n}
  \int_a^b\int_a^b\cdots\int_a^b
  \frac{x_1+x_2+\cdots+x_n}{x_1^2+x_2^2+\cdots+x_n^2}
  \,dx_1\,dx_2\cdots dx_n
\end{aligned}
\]
if \(0<a<b<\infty\).

Topic Tags

Uniform Integrability and Truncation Methods