### Author Topic: TT2 Q4 Question for step4  (Read 1674 times)

#### hanyu Qi

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##### TT2 Q4 Question for step4
« on: December 02, 2018, 01:36:30 PM »
Hello everyone, I am wondering why the range of $\theta$ is $[0,\pi]$ instead of $[\pi,0]$.

Then the integral estimation would be $|\int_{\gamma_{\epsilon}} f(z) \text{d}z| \leq \int_{\pi}^{0} |f(z)| \text{d}z = \frac{-\pi \epsilon}{\sqrt{\epsilon} (1-{\epsilon}^2)}$ goes to 0 as $\epsilon$ close to 0+.

« Last Edit: December 02, 2018, 01:38:14 PM by Alex Qi »

#### hanyu Qi

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##### Re: TT2 Q4 Question for step4
« Reply #1 on: December 02, 2018, 01:41:20 PM »
Never mind. I think I know why.

In the answer, f(z) is integral over $-\gamma_{\epsilon}$. I guess this is why its range is $[0,\pi]$