Look for help with the following GRE questions
Question 1. If $C$ is the circle in the complex plane whose equation $|z|=\pi$, oriented counterclockwise, find the value of the integral $\oint_C(\cos z-z\cos\frac{1}{z})dz$.
Question 2. How to show the sequence $\{x_n\}_{n=1}^\infty$ definted by $x_{n+1}=\frac{1}{2}(x_n+\frac{2}{x_n})$, $x_1\ne 0$ converge.
Question 3. Let $L$ be the curve whose equation in the polar coordinates $r$ and $\theta$ is $r^2=4\cos 2\theta$. Fine the largest value of $y$ such that the point with rectangular coordinates $(x,y)$ is on $L$.
Question 4. Consider the set $S$ of all real-valued functions defined on $[a, b]$, $a. Is it true that if the inverse of $f$ is a constant function, then $f$ is a constant function?