Let z = x+iy and f(2)=√√|xy|. Show that ƒ(z) satisfies the Cauchy-Riemann equations at the origin, but the derivative at the origin does not exist.

Q: Calculate S(102, 100) and s(5, 2) where S(p, k) is the Stirling number of the second kind and s(p,…

A:

Q: Use mathematical induction to prove и исин) {i= VEN 2 1 = 1

A:

Q: Simpson 1/3 rule for integration is mainly based upon the idea of (a) Approximating f(x)in I=ff(x)dx…

A: We need to find the idea behind Simpson  13 rd rule.

Q: .Using 1 – node Gaussian integration, we have ſ ƒ(x) dx ≈ w₁ƒ (x₁). What is the value of x₁ ? b+a…

A:

Q: 3. Given that sin x = and cos y = - -17, such that both x and y are in the same quadrant. Without…

A:

Q: Example 8.10. Evaluate by using (i) Trapezoidal rule, 1+ (ii) Simpson's 1/3 rule, (iii) Simpson's…

A: To evaluate ∫06dx1+x2 Using  (i) Trapezoidal rule (ii) Simpson's 1/3 Rule (iii) Simpson's 3/8 Rule.…

Q: Check the boxes in the accompanying figures to indicate which regions should be shaded to repr (a)…

A: Solution a: Given A∩B∩Cc=A∩B∩U-C So shaded region will be

Q: a, bez show that 19-612 lal-lb/

A: Note: We have the triangle inequality of real numbers as  |x+y| <= |x| + |y| for any two real…

Q: 2. Use the given number of partitions to calculate the Right Endpoint Riemann Sum, and sketch the…

A: Given function is f(x)=cos(x), 0,π2 So graph is Here n=4, it means, we have to divide interval 0,π2…

Q: Compute fdx, where f(x)= | x | .

A:

Q: Using 1 - node Gaussian integration, we have f f(x) dx ≈ w₁f(x₁). What is the value of w₁ ? b+a (a)…

A: Given that using 1-node Gaussian integration, we have…

Q: NOTE: When using interval notation in WeBWork, remember that: You use 'INF' for ∞o and '-INF' for…

A: Given is a function f(x)=x9-9x   (a) To Find: Critical numbers of f. (b) To Determine: Intervals on…

Q: Sketch the region bounded by the graph of the equations and find the area of the region. x = y² -…

A: Solution

Q: Use the root test to determine whether the series 7n n6.5n+1 converges or diverges. n=1

A:

Q: Question 2 Consider the two functions f(x)=1-x² g(x) = x² - 1. (a) Find the intersection points of…

A:

Q: 9. Let (x) and (y) be two sequences converges to c with x y for all n. Assume that f is defined for…

A:

Q: What is the missing number? * 15 17 1 9 8 12 27 40 00 00 28 12 23 13 ? 28

A:

Q: Let X and U be Banach spaces, let C: X→ U be a compact linear map, and let xnx in X. Show that Can →…

A:

Q: 4. True/False: curl(divF)) is not a meaningful expression. (Justify your answer.)

A: Relation between Crul and div of vector quantities

Q: Determine the value of z in the below equation, giving the answer in the form x + yi. z-8=i (7-2z)

A: Solution

Q: Question 9 Calculate the indefinite integral below, with the method of u-substitution. In x [112 dx…

A:

Q: 1. For the following directed graph, find the shortest path from note 1 to note 9. Please show each…

A:

Q: Suppose that in the interval 9 ≤ x ≤ 20 you know that f'(x) is negative and f''(x) is negative.…

A: Given that,In the interval 9≤x≤20,f'(x) is negative.f''(x) is negative.The below quantities are…

Q: Determine the value of z in the below equation, giving the answer in the form x + yi. z-8=i (7 + 2z)

A:

Q: Determine the value of z in the below equation, giving the answer in the form x + yi. z-8=i (7-2z)

A:

Q: = √3+i. Find log z and Log z. Let z = √

A:

Q: Determine the solution(s) to x that satisfy the following equation: (x² + 5x + 5)(x²-6x+5) = 1 HINT:…

A:

Q: Find the solution for series solution.) d²y dy 2t + 4y = 0 with the initial conditions y(0) = 1,…

A:

Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) csch x 8118

A:

Q: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

A:

Q: Find the area of the shaded region. f(x)=x4 -8x³ +24x², g(x) = 5x +38 The area is (Type an integer…

A:

Q: 5. 1 S² + 4s +8 6. 3 (2s+5)³

A:

Q: Using Gaussian integration, (a) 2 ¹₁ f(2x + 3) dx (c) 3 ¹₁ f(3x + 2) dx the integral ff(x) dx is…

A:

Q: Question 1 Let f(x) = x + √x. Find f'(1) at x = 1. A) 0 B) 1+ 2√ C) y = + ³/ D) 1/ E) /

A: Given f(x)=x+x   To Find: f'(1)

Q: 10 inches 6 inches 18 inches Using the dimensions from the previous item, find the rate of change in…

A: Given total surface area formula of rectangular solid SA=2lw+2lh+2wh   ......(1) where l,w,h are the…

Q: Prove both sides equal πU (PN ₂) = (π Up) N (π UV).

A:

Q: d) Z=Sn (PUS) n(QUS) n P n Q n S

A:

Q: Exercise 15.2.21. For each of the following multiplication tables, fill in the blanks to make a…

A: To make a group in caley table , every element in that group appear in each  row and each column…

Q: 6. If a series Eu, converges to the sum u then so does any series obtained from Eu, by rouping the…

A:

Q: Use the method of Lagrange multipliers to optimize the function subject to the given constraint.…

A:

Q: Example 7.22. Find the distance moved by a particle and its acceleration at the end of 4 seconds, if…

A: Legranges interpolation

Q: (1-9²) dx + (1+x¹) dy = 0 2x² dy dx csc (X) ý xe VX-2 =

A: The given differential equations are solved as shown below.

Q: Q1): The concentration of salt is given as a function of time by: dx -37.5-3.5x dt at the initial…

A:

Q: Let u be the solution to the initial boundary value problem for the Heat Equation, d,u(t, x) = 5…

A: Given that ut=5uxx,               0<x<5,   t>0u0,t=0,       u5,t=0,     ux,o=fx=0,…

Q: H-w.4 Find the volumes for the following solids whose heights are defined by E (x,y) and bases are…

A: Volume bounded by xy-plane plane.

Q: et f(x) = 2x6. Compute = coño + C₁7₁ for the domain

A: Given,          f(x)=2x6 To find:        φ^=c0π0+c1π1 for the domain 0≤x≤1 And  π0=x,   π1=x2

Q: Your Task: ● Choose any 3 items that you can measure using Your Hand as an estimate. Use the hand,…

A:

Q: Find the volumes for the following solids whose heights are defined by Z(x,y) and bases are the…

A: Volume bounded by xy-plane plane.

Q: 1) A fair coin is flipped 10 times. What is the probability that exactly 4 of the 10 flips come up…

A: Binomial distribution:  Let p = probability of success on a single trial and n= number of trials.…