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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2019 • Question 7

Question

Math 6420 • PDE Spring 2019 • Question 7

The following function \(f(x)\) [\(x\) is a real variable] is expanded in a series in powers of \((x+3)\). Find the radius of convergence of the series in each case. \[ \begin {array}{rcl} \text {(a)}\quad f(x)&=&e^{x^2},\\[1.4ex] \text {(b)}\quad f(x)&=&\left (\dfrac {\sin x-3}{\sin x-2}\right )^2,\\[1.8ex] \text {(c)}\quad f(x)&=&\dfrac {\sin (x+1)}{(x+1)(x+3)}. \end {array} \]

Raw LaTeX

The following function \(f(x)\) [\(x\) is a real variable] is expanded in a series in powers
of \((x+3)\). Find the radius of convergence of the series in each case.
\[
\begin{array}{rcl}
\text{(a)}\quad f(x)&=&e^{x^2},\\[1.4ex]
\text{(b)}\quad f(x)&=&\left(\dfrac{\sin x-3}{\sin x-2}\right)^2,\\[1.8ex]
\text{(c)}\quad f(x)&=&\dfrac{\sin(x+1)}{(x+1)(x+3)}.
\end{array}
\]

Topic Tags

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