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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2019 • Question 10

Question

Math 6420 • PDE Fall 2019 • Question 10

Find the leading non constant behavior as \(x\to 0^+\) of \[ \int _1^\infty \cos (xt)t^{-1}\,dt. \] You must express the constant term in terms of known quantities and/or constants.

Raw LaTeX

Find the leading non constant behavior as \(x\to0^+\) of
\[
  \int_1^\infty \cos(xt)t^{-1}\,dt.
\]
You must express the constant term in terms of known quantities and/or constants.

Topic Tags

Linear Programming and Optimization Watson's Lemma and Laplace's Method