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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2009 • Question 10

Question

Math 6420 • PDE Fall 2009 • Question 10

Obtain the first two terms of the asymptotic expansion of \[ I(k)=\int _0^5 \frac {e^{-kt}}{\sqrt {t^2+2t}}\,dx, \qquad k\text { is real and } k\to +\infty . \]

Raw LaTeX

Obtain the first two terms of the asymptotic expansion of
\[
  
  I(k)=\int_0^5 \frac{e^{-kt}}{\sqrt{t^2+2t}}\,dx,
  \qquad k\text{ is real and } k\to+\infty.
\]

Topic Tags

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