## Question

###### Evaluate the following integrals22_22$ dz (2+1)2(22+4)cis the circle Iz| = 5[9]4-32$ (Z(2-1)(2-2) dz _ cis the circle Iz/ = 3[6]Find the harmonic conjugate function of u = e-3xcos(3y). Hence show that analytic function f(z) = e-3z + ik where k is a constant [10]

Evaluate the following integrals 22_22 $ dz (2+1)2(22+4) cis the circle Iz| = 5 [9] 4-32 $ (Z(2-1)(2-2) dz _ cis the circle Iz/ = 3 [6] Find the harmonic conjugate function of u = e-3xcos(3y). Hence show that analytic function f(z) = e-3z + ik where k is a constant [10]

## Answers

#### Similar Solved Questions

5 answers

##### 2. (4 points)} Fir:l the JecobiazLne " trens_o-nati3n

2. (4 points)} Fir:l the Jecobiaz Lne " trens_o-nati3n...

3 answers

##### Estimate the minimum number of subintervals to approximate the value of3 sin (X + 4)dx with an errorof magnitude less than 2x 10 "4 using a. the error estimate formula for the Trapezoidal Rule_ b. the error estimate formula for Simpson's Rule.

Estimate the minimum number of subintervals to approximate the value of 3 sin (X + 4)dx with an error of magnitude less than 2x 10 "4 using a. the error estimate formula for the Trapezoidal Rule_ b. the error estimate formula for Simpson's Rule....

5 answers

##### Suppose the time to take Test 2 has a histogram that is left skewed with a mean of 45 minutes and a standard deviation of 5 minutes. If you randomly select 36 students, which of the following statements is true?Select one:The mean of the sampling distribution is 9 minutes The shape of the sampling distribution is normally distributed: The standard error of the sampling distribution is 5 minutes_None of these statements are true_If the sample size is increased, the standard error will increase.

Suppose the time to take Test 2 has a histogram that is left skewed with a mean of 45 minutes and a standard deviation of 5 minutes. If you randomly select 36 students, which of the following statements is true? Select one: The mean of the sampling distribution is 9 minutes The shape of the sampling...

5 answers

##### 24 Energy _ calculations from wavelength or frequency_ Determine the energy (in ) /photon) of 1023nm lightDetermine the energy (in kJJofa red laser that delivers a 3.56 x1027 photons of 652.7 nm lightA new ultra violet laser deliver 3334.5 kJ of energy using light with a wavelength of 247.6 nm, how many photons of light is needed in this laser pulse?

24 Energy _ calculations from wavelength or frequency_ Determine the energy (in ) /photon) of 1023nm light Determine the energy (in kJJofa red laser that delivers a 3.56 x1027 photons of 652.7 nm light A new ultra violet laser deliver 3334.5 kJ of energy using light with a wavelength of 247.6 nm, ho...

3 answers

##### Exercise 8. This exercise outlines a proof - that Euler' $ constant = 2.718281828459045235360287471352662497757247093699959574is irrational. For this problem, you may use the standard integral rules from Calculus. (i) Let In = Jd x"e" dx for n = 0,1,2, Use induction to prove that there are an, bn â‚¬ Z such that In = @n + bne. (ii) Suppose that e = p/q for some p, q â‚¬ N. Show that 0 < < In < n+l and arrive at a contradiction. Conclude that e is irrational.

Exercise 8. This exercise outlines a proof - that Euler' $ constant = 2.718281828459045235360287471352662497757247093699959574 is irrational. For this problem, you may use the standard integral rules from Calculus. (i) Let In = Jd x"e" dx for n = 0,1,2, Use induction to prove that the...

5 answers

##### (1) Compute the anti-derivative of the following functions: for' 4sin(x) + 2) dx(6) f -8e" dx(c) fk-6sec"() +2-') dc(d) fo-r +2-4/2) dx

(1) Compute the anti-derivative of the following functions: for' 4sin(x) + 2) dx (6) f -8e" dx (c) fk-6sec"() +2-') dc (d) fo-r +2-4/2) dx...

5 answers

##### (1 point) Write X product X = E Ez Ez of elementary matrices_EjEzC Ez

(1 point) Write X product X = E Ez Ez of elementary matrices_ Ej Ez C Ez...

5 answers

##### @uesdou 11what is the current in a 70-W lightbulb in a socket supplied with 120v?0.58 AS0 A227A17A8400 APrevious

@uesdou 11 what is the current in a 70-W lightbulb in a socket supplied with 120v? 0.58 A S0 A 227A 17A 8400 A Previous...

5 answers

##### The chapter sections to review are given in parentheses at the end of each question.Indicate if each of the bases in problem 17.57 is found in DNA only, RNA only, or both DNA and RNA. ( 17.1 )

The chapter sections to review are given in parentheses at the end of each question. Indicate if each of the bases in problem 17.57 is found in DNA only, RNA only, or both DNA and RNA. ( 17.1 )...

5 answers

##### Sum of squares What two nonnegative real numbers $a$ and $b$ whose sum is 23 maximize $a^{2}+b^{2} ?$ Minimize $a^{2}+b^{2} ?$

Sum of squares What two nonnegative real numbers $a$ and $b$ whose sum is 23 maximize $a^{2}+b^{2} ?$ Minimize $a^{2}+b^{2} ?$...

5 answers

##### Ages of Proofreaders At a large publishing company, the mean age of proofreaders is 36.2 years, and the standard deviation is 3.7 years_ Assume the variable is normally distributed_ Use TI-83 Plus/TI-84 Plus calculator and round the final answers to at least four decimal places_Part 1 of 2If a proofreader from the company is randomly selected, find the probability that his or her age will be between 35.4 and 36.9 years_P (35.4<X<36.9) 0.1624Part: 1 / 2Part 2 of 2If a random sample of 15 pr

Ages of Proofreaders At a large publishing company, the mean age of proofreaders is 36.2 years, and the standard deviation is 3.7 years_ Assume the variable is normally distributed_ Use TI-83 Plus/TI-84 Plus calculator and round the final answers to at least four decimal places_ Part 1 of 2 If a pro...

5 answers

##### The test statistic of z = 1.77 is obtained when testing the claim that p = 1/2 a. Using a significance level of & = 0.10,find the critical value(s). b. Should we reject Ho or should we fail to reject Ho ` Clickhere to_view_page of the standard normal distribution table Click here to_view_page 2 of the standard normal distribution tablea. The critical value(s) islare z = (Round to two decimal places as needed. Use a comma to separate answers as needed:)

The test statistic of z = 1.77 is obtained when testing the claim that p = 1/2 a. Using a significance level of & = 0.10,find the critical value(s). b. Should we reject Ho or should we fail to reject Ho ` Clickhere to_view_page of the standard normal distribution table Click here to_view_page 2 ...

5 answers

##### Chapter 4, Section 4.6, Supplementary Question 01Find the coordinate vector for p relative to S = {p1 pz pz} p = 5 - Sx + x2; Pi = 1, Pz = X, P3 = x2 [pJs

Chapter 4, Section 4.6, Supplementary Question 01 Find the coordinate vector for p relative to S = {p1 pz pz} p = 5 - Sx + x2; Pi = 1, Pz = X, P3 = x2 [pJs...

5 answers

##### SaveExit Certify Lesson: 4 1 Relations and FunctonsQOuesrionof 9, stCpconrectDetermine g6 -R(x) for the following Fundors() = 42AnsweE( + 4) RG)Gro7oHaute Lcamnine

Save Exit Certify Lesson: 4 1 Relations and Functons QOuesrion of 9, stCp conrect Determine g6 - R(x) for the following Fundor s() = 42 Answe E( + 4) RG) Gro7oHaute Lcamnine...

1 answers

##### Consider the linear transformation T(x, Y, 2) = (3x + Y + Sz,x _ 2y+ 22,(4 _ a)y) where a is a constant and a # 4a) [2 marks] Show that T is linear by finding the standard matrix associated with Tb) [2 marks] Find the image of (~3,0,3) under T .c) [1 marks] Let A be the standard matrix associated with T Prove that A is invertible then find A-1_[3 marks] Find the pre-image of (5,3,0) under T _

Consider the linear transformation T(x, Y, 2) = (3x + Y + Sz,x _ 2y+ 22,(4 _ a)y) where a is a constant and a # 4 a) [2 marks] Show that T is linear by finding the standard matrix associated with T b) [2 marks] Find the image of (~3,0,3) under T . c) [1 marks] Let A be the standard matrix associated...

5 answers

##### The ext few problems uses the function f : (0,1) 4 (0,1) that we HOW define: If a â‚¬ (0,1). let (k;)i, be decimal expansion for with the choice of the one ending in (000o if a â‚¬ E, define f (a) CiIT5- (So; for example f(0.123) 0.010203.What is f(1/3) as a fraction? 6. Show that f is continous at a if and only if a â‚¬ E. (Hint: estimate |f (a) _ f(6)| if a.b have the same first digits in their decimal expansion_

The ext few problems uses the function f : (0,1) 4 (0,1) that we HOW define: If a â‚¬ (0,1). let (k;)i, be decimal expansion for with the choice of the one ending in (000o if a â‚¬ E, define f (a) CiIT5- (So; for example f(0.123) 0.010203. What is f(1/3) as a fraction? 6. Show that f is con...

5 answers

##### Suppose fn 7f uniformly on set S and gn 9 uniformly on S. Recall the definition that fn 7f uniformly on S. (You do not need to write this down: This only serves as a hint for next parts:) (b) Use the definition in a) to show that fn + In - f + g uniformly on S.(c) Suppose h S _ R is a bounded function. Is fnh 7 fh uniformly on S? Justify your answer_

Suppose fn 7f uniformly on set S and gn 9 uniformly on S. Recall the definition that fn 7f uniformly on S. (You do not need to write this down: This only serves as a hint for next parts:) (b) Use the definition in a) to show that fn + In - f + g uniformly on S. (c) Suppose h S _ R is a bounded funct...