- #1

Jenny short

- 3

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$$\lim_{U\rightarrow\infty}\int_C \frac{ze^{ikz}}{z^2+a^2}dz = 0 $$

Where $$R>2a$$ and $$k>0$$ And C is the curve, defined by $$C = {x+iU | -R\le x\le R}$$

I have tried by using the fact that

$$|\int_C \frac{ze^{ikz}}{z^2+a^2}dz| \le\int_C |\frac{ze^{ikz}}{z^2+a^2}|

|dz|$$

I want to use the fact $$|e^{ikz}|=e^{-kU}$$

However I got really stuck after that. I would really appreciate help