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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2014 • Question 6

Question

Math 6420 • PDE Fall 2014 • Question 6

Find the radius of convergence of the Taylor series with the center at \(x_0=1\) for the following function

  1. \[ f(x)=x^{1/3} \]
  2. \[ f(z)=\frac {(\sin x+2)^2}{(\sin x-2)^2} \]

(\(x\) 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 \(x_0=1\) for the
following function
\begin{enumerate}
\item[(a)]
\[
  f(x)=x^{1/3}
\]

\item[(b)]
\[
  f(z)=\frac{(\sin x+2)^2}{(\sin x-2)^2}
\]
\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