7. Cauchy Integral Formula

Derivatives Of Analytic Functions — Quiz

Test your understanding of derivatives of analytic functions with 5 practice questions.

Practice Questions

Question 1

Which formula gives $f'(z_0)$ when $f$ is analytic on and inside a positively oriented simple closed contour $C$ that contains $z_0$?

Question 2

Which formula gives the $n$th derivative $f^{(n)}(z_0)$ under the Cauchy integral formula?

Question 3

If $f$ is analytic in a domain, which statement is true about its derivative?

Question 4

Evaluate $\frac{1}{2\pi i}\int_{|z|=3}\frac{z^2+1}{(z-1)^2}\,dz$.

Question 5

If $f$ is analytic on and inside $|z-z_0|=2$ and $|f(z)|\le 5$ on the circle, what is a bound for $|f'(z_0)|$?