Answer:
9πi/2
Step-by-step explanation:
![\oint\limits_C {\frac{5z^{2}+4}{(z-1)(z+3)} } \, dz,\ C: |z|=2](https://tex.z-dn.net/?f=%5Coint%5Climits_C%20%7B%5Cfrac%7B5z%5E%7B2%7D%2B4%7D%7B%28z-1%29%28z%2B3%29%7D%20%7D%20%5C%2C%20dz%2C%5C%20C%3A%20%7Cz%7C%3D2)
Let f(z) = (5z² + 4) / (z + 3).
![\oint\limits_C {\frac{f(z)}{z-1} } \, dz,\ C: |z|=2](https://tex.z-dn.net/?f=%5Coint%5Climits_C%20%7B%5Cfrac%7Bf%28z%29%7D%7Bz-1%7D%20%7D%20%5C%2C%20dz%2C%5C%20C%3A%20%7Cz%7C%3D2)
Using Cauchy's integral formula:
![2\pi i\ f(1)\\2\pi i\ (\frac{5(1)^{2}+4}{1+3}) \\2\pi i\ (\frac{9}{4}) \\\frac{9\pi i}{2}](https://tex.z-dn.net/?f=2%5Cpi%20i%5C%20f%281%29%5C%5C2%5Cpi%20i%5C%20%28%5Cfrac%7B5%281%29%5E%7B2%7D%2B4%7D%7B1%2B3%7D%29%20%5C%5C2%5Cpi%20i%5C%20%28%5Cfrac%7B9%7D%7B4%7D%29%20%5C%5C%5Cfrac%7B9%5Cpi%20i%7D%7B2%7D)
Standard form: 7z^4-6z^2-6z
This IS a polynomial, it's degree is 4 and has 3 terms
Answer:
The first option.
Step-by-step explanation:
Answer:
|2x|
Step-by-step explanation:
The square root symbol indicates the positive square root. That is, ...
![\sqrt{x^2}=|x|](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%7D%3D%7Cx%7C)
Then the square root you show is ...
![\sqrt{(-2x)^2}=|{-}2x|=\boxed{|2x|}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-2x%29%5E2%7D%3D%7C%7B-%7D2x%7C%3D%5Cboxed%7B%7C2x%7C%7D)
Answer:
-23/4
Step-by-step explanation:
![-5\frac{3}{5}](https://tex.z-dn.net/?f=-5%5Cfrac%7B3%7D%7B5%7D)
![-\frac{5x4+3}{4}](https://tex.z-dn.net/?f=-%5Cfrac%7B5x4%2B3%7D%7B4%7D)
![-\frac{20+3}{4}](https://tex.z-dn.net/?f=-%5Cfrac%7B20%2B3%7D%7B4%7D)
![-\frac{23}{4}](https://tex.z-dn.net/?f=-%5Cfrac%7B23%7D%7B4%7D)