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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2015 • Question 6

Question

Math 6420 • PDE Spring 2015 • Question 6

Find the radius of convergence of the Taylor series with the center at the origin (\(x_0=0\)) for the following function

  1. \[ f(x)=\frac {\sqrt {x+3}}{x^2+3} \]
  2. \[ f(x)=\frac {1}{(\cos x+3)^2} \]

(\(x\) is a real variable; you do not need to find the series themselves).

Raw LaTeX

Find the radius of convergence of the Taylor series with the center at the origin
(\(x_0=0\)) for the following function
\begin{enumerate}
\item[(a)]
\[
  f(x)=\frac{\sqrt{x+3}}{x^2+3}
\]

\item[(b)]
\[
  f(x)=\frac{1}{(\cos x+3)^2}
\]
\end{enumerate}
(\(x\) is a real variable; you do not need to find the series themselves).

Topic Tags

Consistency, Stability, and Convergence Forward Euler and First-Order Convergence Linear Programming and Optimization Variable-Coefficient Diffusion Problems