Use the theorem in Sec. 28 to show that if f (z) is analytic and not constant throughout a domain D, then it cannot be constant throughout any neighborhood lying in D. Suggestion: Suppose that f(z) does have a constant value ωo throughout some neighborhood in D.

Answers

Answer 1

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.


Related Questions

Please explain step by step I dont get it.

Answers

Answer: B

Step-by-step explanation:

108 divide by 54 = 2

That equation means she paid 2 dollars per ticket, not 1 dollar for 2 tickets

(There is no 1 in the equation also)

Find the volume of the pyramid.

Please Help!

Answers

Answer:

144cm

Step-by-step explanation:

Just search it up lol

One hundred forty four centimeters

Find the Perimeter of this figure. I do y get it

Answers

Answer:

56m

Step-by-step explanation:

5+7+5+11+7+16+5

= 56

Well to find the perimeter of any shape all you have to do is add the lengths of all the sides. In this problem the lengths of the sides are 5 + 5 + 5 + 11 + 7 + 16 + 7 which equals 56. So the perimeter of this shape is 56 m. Hope this helps!

Find mean & margin of error if 28.4 < µ < 38.8

Answers

Answer:

The mean is of 33.6

The margin of error is of 5.2.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this question:

Lower bound: 28.4

Upper bound: 38.8

Mean

(28.4+38.8)/2 = 33.6.

The mean is of 33.6

Margin of error:

(38.8 - 28.4)/2 = 5.2

The margin of error is of 5.2.

The groundhog population of​ Punxsutawny, Pennsylvania is closely monitored each year. Two years ago the population decreased by​ 12%. Last year the number of groundhogs increased by​ 6%. This year the population also increased by​ 9%. What was the percentage​ increase/decrease of groundhogs over these three​ years? Round your answer to the nearest tenth of a percentage poin

Answers

Answer:

There was a increase of 1.7% over these three​ years

Step-by-step explanation:

Multipliers:

For a decrease of a%, we multiply by: [tex]\frac{100-a}{100}[/tex]

For a increase of a%, we multiply by: [tex]\frac{100+a}{100}[/tex]

What was the percentage​ increase/decrease of groundhogs over these three​ years?

Decrease of 12%(multiplication by 0.88).

Increase of 6%(multiplication by 1.06).

Increase of 9%(multiplication by 1.09).

After these three years:

0.88*1.06*1.09 = 1.017

1.017 - 1 = 0.017

0.017*100% = 1.7%

There was a increase of 1.7% over these three​ years

The length of a rectangle is 2 meters longer than the width. If the area is 30 square meters, find the rectangle's dimensions.

Answers

the answer would be 15
30 divided by 2
if it’s wrong I’m so sorry.

Will give the brainliest answer and 20 points to anyone who can give a complete answer and not a scam link or a joke answer or begging for points (those 3 types of answers will be reported)

Courtney and Christy both leave the coffee shop at the same time, but in opposite directions. If Christy travels 9 mph faster than Courtney and after 7 hours they are 189 miles apart, how fast is each traveling?

Courtney is traveling ___________ mph.

Christy is traveling _____________ mph.

Answers

Answer:

Courtney is travelling at 9mph

Christy is travelling at 18mph

Step-by-step explanation:

Courtney's speed = x

Christy's speed = y

Christy travels 9 mph faster than Courtney: x+9=y

Distance = speed * time

Courtney's distance after 7 hours = 7x

Christy's distance after 7 hours = 7y

After 7 hours, they're 189 miles apart:

7x+7y=189

x+y=27

x+y=27

x+x+9=27

2x=18

x=9

y=x+9

y=9+9

y=18

What is the equation of the following line?

Answers

The the the the the the the answer is of course 3

Answer:

Answer is F. y = 6x

Step-by-step explanation:

Evaluate the piecewise function when x = -1.

Answers

Step-by-step explanation:

-2<-1<1, so f(-1)=-1-2=-3

There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest inch, how many inches are in 8 meters?

Answers

Answer:

314.96in

Step-by-step explanation:

A rectangular pool is being constructed with a length that is four times the width. There will be a walkway constructed around the pool that is 6 feet wide all around. Write a factored expression for the area in square feet of the pool and the walkway combined.

Answers

Answer:

(4x²+36) feet²

Step-by-step explanation:

Area of the pool = L × W

Take width as x and Length as 4x

4x × x = (4x²)feet² {area of pool}

Area of walkway = L × W

6 × 6 = 36feet²

Total area = 4x² + 36 feet²

At 3:30 p.m., you have 15 megabytes of a movie. At 3:45 p.m., you have 75 megabytes. What is the download rate in megabytes per minute?

Answers

The answer would be 2 megabytes a minute

Can someone help me with this problem please. ( I need it as fast as possible).

Answers

Answer:

D-B-A-C

Step-by-step explanation:

The net of a triangular prism is shown
below.
8.5 cm
10 cm
10 cm
10 cm
What is the total surface area of the prism?
A 470 cm?
C 390.5 cm?
B 385 cm
D 342.5 cm

Answers

Answer:

i think a.... sorry if im wrong

Step-by-step explanation:

Will give brainliest

Answers

Answer: Because the question uses the word “distinct” meaning obvious, and clear, I would select AB, AC, CB. (If it’s asking for all the possible line segments, I would select AB, AC, CB, BA, CA, BC).

Which function is continuous at x = –4?

Answers

Answer:

The correct answer is C. I tried B and got it wrong

Step-by-step explanation:

A quarter has a diameter of 24 mm.
Which measurement is closest to the
circumference of the quarter in
millimeters?
A. 452.39 mm
B. 37.7 mm
C. 75.4 mm
D. 150.8 mm

Answers

Answer:

C or D

Step-by-step explanation:

4. Let's say we do an opinion poll and find that 56% of the people say the Green Bay Packers
are their favorite team, while 22% choose the Chicago bears, and 10% choose the Dallas
Cowboys. What percent of people must have a favorite team other than these three teams?

Answers

56+22+10 = 98
100 - 88 = 12
12% of people have a favorite team other than the three teams

40 POINTS!!!

Two construction companies are building homes in a new neighborhood. Company A has built 18 homes and plans to build an additional 6 homes each month. Company B has built 41 homes and plans to build an additional 4 homes each month. if building goes according to their plans, in how many months will the total number of homes built by the companies be equal to each other?

Answers

Answer:

14 months until there equal

Answer:

14 months

Step-by-step explanation:

Helppppp plzzzzzzz!!!!! 15+PTS and brainliest!!!!!!!!! ASAP plzzz!!!!!!!!

Answers

Answer:

75 FT

Step-by-step explanation:

Multiple 5 by 4 for each of the three squares, then multiply 5 by 3 for each triangle and divide it by 2. Add them all together and you get 75.

Answer:

75 Ft

Step-by-step explanation:

I told you im surewhwhwhhwhshsbsbwbsbsbsbs

Mario traced this trapezoid.

Answers

Answer:

84sq. in

Step-by-step explanation:

Area of the rectangle  = length * width

Given

Length = 7in

Width = 12in

Area of the rectangle = 7in * 12in

Area of the rectangle = 84sq. in

Hence the area of the rectangle is 84sq. in

What do those emojis mean in words?

Answers

Dark barking up no tree?

A black hole

The last one ...a girl playing a instrument

If a•b=b, what must the value of a be?
A.1
B.0
C.2
D.b

Answers

Answer:

a

Step-by-step explanation:

an example

1x2=2

1 is a, 2 is b, see they equal the same 2 and 2.

Answer:

B. 0

Step-by-step explanation:

Any number multiplied by 0 equals zero.

ted is twice his sister's age and three years younger than joe. ted's sister is half of a century plus ten. how old is ted how old is ted's sister​

Answers

Answer:

120, 60

Step-by-step explanation:

half a century = 60 + 10 x 2 = ted.

she is 60.

In each case, calculate the circumference and the area.
The radius is 22 cm.
Your answer​

Answers

Answer:

Circumference of circle = 138.28 cm (Approx.)

Area of circle = 1,521.11 cm² (Approx.)

Step-by-step explanation:

Given:

Radius of circle = 22 cm

Find:

Circumference of circle

Area of circle

Computation:

Circumference of circle = 2πr

Circumference of circle = 2(22/7)(22)

Circumference of circle = 2(3.1428)(22)

Circumference of circle = 138.2832

Circumference of circle = 138.28 cm (Approx.)

Area of circle = πr²

Area of circle = (22/7)(22)²

Area of circle = (3.1428)(22)(22)

Area of circle = 1,521.1152

Area of circle = 1,521.11 cm² (Approx.)

Find the value of y. geometry!!

Answers

Answer:

y = 54

Step-by-step explanation:

Once again we are going to use the inscribed angle and intercepted arc relationship where the inscribed angle is equal to half of the measure of the intercepted arc.

Angle "y" is the inscribed angle and its intercepted arc has a measure of 108°

So y = one half of 108

[tex]\frac{108}{2} =54[/tex]

So we can conclude that y = 54

Please help me 7th grade math math

Answers

Answer: 1/8

Step-by-step explanation: hoped this helped:))

Answer:

i think its 1/3

Step-by-step explanation:

Help please I’ll give extra points and brainlist

Answers

Answer:

Step-by-step explanation:

Probably D,  he's measuring voltage across the wire.. and then across the light bulb,   there would be very little across the wire and a lot across the light bulb

A 1/17th scale model of a new hybrid car is tested in a wind tunnel at the same Reynolds number as that of the full-scale prototype. The drag coefficient of the model is the same as that of the prototype. Assuming the model and prototype are both tested in air, find the ratio of the drag on the scale model (Fm) to the drag on the prototype (Fp), i.e., Fm/Fp. Since the size of the model is 1/17th of the size of the prototype, the projected area of the model is (1/17)2 of the projected area of the prototype. Round your answer to the nearest tenth.

Answers

Answer:

The ratio of the drag coefficients [tex]\dfrac{F_m}{F_p}[/tex] is approximately 0.0002

Step-by-step explanation:

The given Reynolds number of the model = The Reynolds number of the prototype

The drag coefficient of the model, [tex]c_{m}[/tex] = The drag coefficient of the prototype, [tex]c_{p}[/tex]

The medium of the test for the model, [tex]\rho_m[/tex] = The medium of the test for the prototype, [tex]\rho_p[/tex]

The drag force is given as follows;

[tex]F_D = C_D \times A \times \dfrac{\rho \cdot V^2}{2}[/tex]

We have;

[tex]L_p = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2 \times L_m[/tex]

Therefore;

[tex]\dfrac{L_p}{L_m} = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2[/tex]

[tex]\dfrac{L_p}{L_m} =\dfrac{17}{1}[/tex]

[tex]\therefore \dfrac{L_p}{L_m} = \dfrac{17}{1} =\dfrac{\rho _p}{\rho _p} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_p} \right)^2 = \left(\dfrac{V_p}{V_m} \right)^2[/tex]

[tex]\dfrac{17}{1} = \left(\dfrac{V_p}{V_m} \right)^2[/tex]

[tex]\dfrac{F_p}{F_m} = \dfrac{c_p \times A_p \times \dfrac{\rho_p \cdot V_p^2}{2}}{c_m \times A_m \times \dfrac{\rho_m \cdot V_m^2}{2}} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}[/tex]

[tex]\dfrac{A_m}{A_p} = \left( \dfrac{1}{17} \right)^2[/tex]

[tex]\dfrac{F_p}{F_m} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}= \left (\dfrac{17}{1} \right)^2 \times \left( \left\dfrac{17}{1} \right) = 17^3[/tex]

[tex]\dfrac{F_m}{F_p} = \left( \left\dfrac{1}{17} \right)^3[/tex]= (1/17)^3 ≈ 0.0002

The ratio of the drag coefficients [tex]\dfrac{F_m}{F_p}[/tex] ≈ 0.0002.

simplify 3 times x² times y times 4z times x times 2y times z​

Answers

Answer:

3(x^2 x Y)(4z x X)(2y x Z)

Step-by-step explanation:

Answer:

[tex]3(x^{3} * 2y^2*4z^2)[/tex]

Step-by-step explanation:

x^2(x) = x^3

2y(y) = 2y^2

4z(z) = 4z^3

Multiple it all by 3

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