2021-8.md

course	course_year	question_number	tags	title	year
Complex Analysis or Complex Methods	IB	8	IB 2021 Complex Analysis or Complex Methods	Paper 1, Section I, B	2021

Let $x>0, x \neq 2$, and let $C_{x}$ denote the positively oriented circle of radius $x$ centred at the origin. Define

$$g(x)=\oint_{C_{x}} \frac{z^{2}+e^{z}}{z^{2}(z-2)} d z$$

Evaluate $g(x)$ for $x \in(0, \infty) \backslash{2}$.