Carry out the following integrals, counterclockwise, around the indicated contour​

Carry Out The Following Integrals, Counterclockwise, Around The Indicated Contour

Answers

Answer 1

For the first integral, z = π/4 is a pole of order 3 and lies inside the contour |z| = 1. Compute the residue:

[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = \lim_{z\to\frac\pi4}\frac1{(3-1)!} \frac{d^{3-1}}{dz^{3-1}}\left[e^z\cos(z)\right][/tex]

We have

[tex]\dfrac{d^2}{dz^2}[e^z\cos(z)] = -2e^z \sin(z)[/tex]

and so

[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = - \lim_{z\to\frac\pi4} e^z \sin(z) = -\frac{e^{\pi/4}}{\sqrt2}[/tex]

Then by the residue theorem,

[tex]\displaystyle \int_C \frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3} \, dz = 2\pi j \left(-\frac{e^{\pi/4}}{\sqrt2}\right) = \boxed{-\sqrt2\,\pi e^{\pi/4} j}[/tex]

For the second integral, z = 2j and z = j/2 are both poles of order 2. The second poles lies inside the rectangle, so just compute the residue there as usual:

[tex]\displaystyle \mathrm{Res}\left(\frac{\cosh(2z)}{(z-2j)^2\left(z-\frac j2\right)^2}, z=\frac j2\right) = \lim_{z\to\frac j2}\frac1{(2-1)!} \frac{d^{2-1}}{dz^{2-1}}\left[\frac{\cosh(2z)}{(z-2j)^2}\right] = \frac{16\cos(1)-24\sin(1)}{27}j[/tex]

The other pole lies on the rectangle itself, and I'm not so sure how to handle it... You may be able to deform the contour and consider a principal value integral around the pole at z = 2j. The details elude me at the moment, however.


Related Questions

The gas tank on a car holds 13.3 gallons. If the car goes 199.5 miles on a single tank, how many miles per gallon does the car get?

Answers

Answer:

292.6

Step-by-step explanation:

will mark brainliest Select the correct answer.
Which relation is a function?
ОА
ху
14 -2
5 -3
6 -2
7-3
ОВ.
ху
310
220
3 30
440
ОС
Х У
-52
-53
-104
-105
OD.
ху
1015
2025
8 30
2035

Answers

mhm so basically 3-2 = 1 which works

what is the value of the expression when a=5, b=4, and c=6?
4a/2b-c

a. 2
b. 5
c. 9
d. 10

Answers

Answer:

D

Step-by-step explanation:

Pluck in the values, we have:

4.5/2.4 - 6 = 20/2 = 10

How do you make a mixed fraction and write it out as a improper fraction?

Answers

Answer:

1) Multiply the whole number part by the fraction's denominator.

2) Add that to the numerator.

3) Then write the result on top of the denominator.

Step-by-step explanation:

Hope this helps!

Answer:

Explanation

|

Step-by-step explanation:

you you multiply the whole number by the denominator and then add the numerator to that number.

In a group of workers, 16 belonged to a lottery syndicate and 4 did not.

What fraction of the workers did not belong to the syndicate?

1: 4/16

2: 1/5

3: 1/4

4: 3/4

Answers

Answer:

HI THERE

the answer is number 1 !!

correct me if I'm wrong

a coffee mug collection includes four red mugs, eight yellow mugs and two white mugs. What is the probability of selecting two white mugs one after another?

Answers

Assuming that the selection process was done without replacement, the probability of selecting two white mugs without replacement is 1/28

Given data

Sample Space

Red mugs = 4

yellow mugs = 8

white mugs = 2

Sample Size = 4+8+2 = 14

We are going to assume the selection was done with out replacement

Hence the probability of selecting the first white mug is

Pr(W1) = 2/8 = 1/4

The probability of selecting the second white mug is

Pr(W2) = 1/7

Hence the probability of selecting  two white mugs one after another

= 1/4*1/7

=1/28

Learn more about probability at:

https://brainly.com/question/25839839

Find the perimeter of the figure. Use 3.14 for 7 and round to at least 1 decimal place.

Answers

Answer:

the perimeter of the figure is 27.4 mi

Step-by-step explanation:

rectangle perimeter = 6+6+6 = 18

half circle perimeter = 1/2 2πr = 3.14 × 3 = 9.42

the perimeter of the figure is 18+9.42 = 27.42 --> 27.4 mi

PLS HELP!!!
Express each of these numbers, as a product of two fractions
1/15

Answers

[tex]\dfrac 13 \times \dfrac 15 = \dfrac 1{15}[/tex]

The product of the two fraction numbers whose result is 1/15 will be 1/3 and 1/5.

What is Algebra?

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The result of the product of the two fraction numbers is given below.

1/15

The factor of the number 15 is given as,

15 = 3 x 5

Then the expression is written as,

1/15 = 1/ (3 x 5)

1/15 = (1/3) x (1/5)

The multiplication of the two rational numbers whose result is 1/15 will be 1/3 and 1/5.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

how can 26n-7m+4(10n-6m)

Answers

Answer:

66n-31m

Step-by-step explanation:

26n-7m+4(10n-6m)

26n-7m+40n-24m

66n-31m

Please confirm my answer to be correct

Answers

Answer:

Actually, Corresponding angles are congruent.

Step-by-step explanation:

They are only supplementary in the special case where they are both 90°

Answer:

Option D

Step-by-step explanation:

Since we know that measure of corresponding angles are equal. So, corresponding angle are congruent to each other

The second step to dividing 3 into 1/2

Answers

Answer:

Change the sign

Step-by-step explanation:

Asumming you are talking about the keep change flip method for dividing fraction, you would 1) keep 3/1, 2) flip the / symbol into * and 3) flip the 2nd fraction

When a number is subtracted from -3 2/3 , the result is -2 1/6. What is the number?
A.5 5/6
B. 1 1/2
C. - 1 !/2
D. -5 5/6

Answers

Answer:

D. [tex]-5 \frac{5}{6}[/tex]

Step-by-step explanation:

Add the values:

[tex]-3\frac{2}{3}+\left(-2\right)\frac{1}{6}[/tex]

[tex]=-\frac{11}{3}+\left(-2\right)\frac{1}{6}[/tex]

[tex]=-\frac{11}{3}-\frac{1}{3}[/tex]

[tex]-5 \frac{5}{6}[/tex]

Answer:

C. - 1 ½

Step-by-step explanation:

-3⅔ - x = - 2⅙

x = -3⅔ + 2⅙

x = -11/3 + 13/6

x = -22/6 + 13/6

x = -9/6

x = -1 ½

6(25-8w)+20w for w=2

Answers

150−28w

i think i dont know

A line that includes the point (0, -2) has a slope of 1. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=1x-2

Step-by-step explanation:

Well this one is already given

When x=0, it's the y intercept

and it gives the slope, so we got it :D

Answer:

y=x-2

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=1(x-0)

y+2=1(x)

y+2=x

y=x-2

Ilana has 70¢ in her purse. All the coins have the same value. What could describe all the coins she has in her purse?

71 pennies
8 dimes
14 nickels
3 quarters

Answers

Answer:

14 nickels is the answer

Step-by-step explanation:

Solve the equation. Show your work!
2. 2m + 1.5 = 3m - 11.7

Answers

Answer:

gek

Step-by-step explanation:

What is an equation of the line that passes through the point (6,-4) and isperpendicular to the line 22 - y = 5?

Answers

y=1/17 maybe cuz perpendicular you change the negative and positive signs and flip the variable and the equation is 22-y=5 which is y=-17 so if you flip it it’s y=1/17

At a school 60% of students buy a school lunch. Only 10% of students buy lunch and dessert. What is the probability that a student who buys lunch also buys dessert?

Answers

Answer:

1/6

Step-by-step explanation:

P(A) = probability a student buys lunch = 60% = 0.6

P(B) = probability a student buys lunch and dessert = 10% = 0.1

We are looking at the probability that a student buys lunch and dessert on the condition that they already bought lunch. Therefore, we are looking at a conditional probability.

P(B given A) = P(A and B) / P(A)

= 0.1 / 0.6

= 1/6 ≈ 0.167

A line includes the points (-7, 1) and (7, -1). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=-1/7x

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-1)/(7-(-7))

m=-2/(7+7)

m=-2/14

simplify

m=-1/7

--------------------

y-y1=m(x-x1)

y-1=-1/7(x-(-7))

y-1=-1/7(x+7)

y=-1/7x-7/7+1

y=-1/7x-1+1

y=-1/7x

How to determine if Triangles are Congruent?


If they are, how do you know if they are SSS or ASA or SAS or AAS?


Essentially, how do I apply the different congruent thermos to the questions attached?

Answers

So basically what you have to do is first identify all of the sides or angles that equal eachother then you can see if you did a side side and side in a row etc, like 44 would be SAS because the vertical angles would be inbetween the two sides. 46 would be SSS because after you make the line in the middle for reflexive property you can see that there are three sides in a row. If this didnt help i recommend looking on Khan Academy

In the New York marathon there were 45 360 runners. 7 /10 of the runners were women. How many of the runners were men? ​

Answers

Answer:

13,608

Step-by-step explanation:

If 7/10 of the runners were women, than 3/10 of the runners were men. 3/10 of 45,360 runners is 13,608.

Hope this helps! Pls give brainliest! Also, plz sub to kgirl633 on yt.

What is the common ratio of the sequence?
-2, 6, -18, 54,...

A.-3
B.-2
C.3
D.8

Answers

-3 bc i know everything

I do not know how to do it

Answers

Neither do I sorry hope you find the correct person

Answer:

this is do confusing I do not understand

Hi need help for this maths question

Answers

a) If f(y) is a probability density function, then both f(y) ≥ 0 for all y in its support, and the integral of f(y) over its entire support should be 1. eˣ > 0 for all real x, so the first condition is met. We have

[tex]\displaystyle \int_{-\infty}^\infty f(y) \, dy = \frac14 \int_0^\infty e^{-\frac y4} \, dy = -\left(\lim_{y\to\infty}e^{-\frac y4} - e^0\right) = \boxed{1}[/tex]

so both conditions are met and f(y) is indeed a PDF.

b) The probability P(Y > 4) is given by the integral,

[tex]\displaystyle \int_{-\infty}^4 f(y) \, dy = \frac14 \int_0^4 e^{-\frac y4} \, dy = -\left(e^{-1} - e^0\right) = \frac{e - 1}{e} \approx \boxed{0.632}[/tex]

c) The mean is given by the integral,

[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \int_0^\infty y e^{-\frac y4} \, dy[/tex]

Integrate by parts, with

[tex]u = y \implies du = dy[/tex]

[tex]dv = e^{-\frac y4} \, dy \implies v = -4 e^{-\frac y4}[/tex]

Then

[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \left(\left(\lim_{y\to\infty}\left(-4y e^{-\frac y4}\right) - \left(-4\cdot0\cdot e^0\right)\right) + 4 \int_0^\infty e^{-\frac y4} \, dy\right)[/tex]

[tex]\displaystyle \cdots = \int_0^\infty e^{-\frac y4} \, dy[/tex]

[tex]\displaystyle \cdots = -4 \left(\lim_{y\to\infty} e^{-\frac y4} - e^0\right) = \boxed{4}[/tex]

How much money does drake make and how many houses does he have

Answers

Answer:

Step-by-step explanation:

Drake has 2 houses and makes $50,000,000

basically how to write y-3=4(x+2) in slope intercept form

Answers

Answer: y = 4x + 11

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Rewrite in slope-intercept form.

Simplify the right side.

Simplify 4(x + 2).

y - 3 = 4x + 8

Move all terms not containing y to the right side of the equation.

Add 3 to both sides of the equation.

y = 4x + 8 + 3

Add 8 and 3.

y = 4x + 11

Your Welcome! :)

i really need help, does anyone know these

Answers

Answer: If angle A is congruent to angle E

in simplest terms: (-5x-7)-(-4x-6)(−5x−7)−(−4x−6)

Answers

Answer:

-20x^2-59x-43

Step-by-step explanation:

Q10. Five t-shirts and a hat cost £83.00. Two t-shirts and a hat cost £38.00. How much does one t-shirt cost?

No spam links and plz write down the answer.

Answers

Step-by-step explanation:

Two t-shirts that are(31.80) plus a hat(6.20) cost £38.00.

which means that one t-shirt costs £15.90 :)

From a sample size of 169, it was determined that the 68% confidence interval for the population mean is (505, 517). Therefore, the sample mean was ___. and the margin of error was ___.

A. 511; 6
B. 511; 12
C. 513; 6
D. 513; 12

Answers

Answer:

A. 511; 6

Step-by-step explanation:

The margin of error would be [tex]\pm\frac{517-505}{2}=\pm\frac{12}{2}=\pm 6[/tex]

The sample mean would be [tex]505+6=511[/tex] (or [tex]517-6=511[/tex])

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