Answer:
The value of f(z) is not constant in any neighbourhood of D. The proof is as explained in the explaination.
Step-by-step explanation:
Given
For any given function f(z), it is analytic and not constant throughout a domain D
To Prove
The function f(z) is non-constant constant in the neighbourhood lying in D.
Proof
1-Assume that the value of f(z) is analytic and has a constant throughout some neighbourhood in D which is ω₀
2-Now consider another function F₁(z) where
F₁(z)=f(z)-ω₀
3-As f(z) is analytic throughout D and F₁(z) is a difference of an analytic function and a constant so it is also an analytic function.
4-Assume that the value of F₁(z) is 0 throughout the domain D thus F₁(z)≡0 in domain D.
5-Replacing value of F₁(z) in the above gives:
F₁(z)≡0 in domain D
f(z)-ω₀≡0 in domain D
f(z)≡0+ω₀ in domain D
f(z)≡ω₀ in domain D
So this indicates that the value of f(z) for all values in domain D is a constant ω₀.
This contradicts with the initial given statement, where the value of f(z) is not constant thus the assumption is wrong and the value of f(z) is not constant in any neighbourhood of D.
Answer:
hello there
ok so the answer is 4 + 
Step-by-step explanation:
hope this helps!
Answer:
Average rate of change: 
Step-by-step explanation:
<u>Remember:</u>
The average rate of change of a function over an interval ![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
is 
<u>Given:</u>
![[a,b]=[1,7]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%3D%5B1%2C7%5D)
<u>Calculation:</u>
Therefore, the average rate of change of the function 
over the interval 
is .
Answer:
-25.5
8x3=24
but we still have the .5 so we multiply that by 3 which equals to 1.5 add that to 24 which makes 25.5 and because only one of the numbers was negative it turns 25.5 into -25.5.
Answer:
22.6 mi
Step-by-step explanation:
The shortest route is to go from bloomington to seaside to westminster. Simply add up the distances along this route.
