2+13 Evaluate zdz along the following paths- I+i2 (a) horizontally from 1+i2 to 2 + i2 then vertically to 2 + i3. (b) vertically from 1 +i to 1 + i3 then horizontally to 2 + i3.

Q: 7. 2xyy' + (x2 – 1)y² = x²e*

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Q: Solve using Gaussian Elimination with back-substitution or Gauss Jordan 000 = 80을 + 20승 - 1루 * - =…

A: Given system of equations, 12x1-37x2+29x3=34963023x1+49x2-25x3=-194545x1-18x2+43x3=139150 The…

Q: THEOREM 4.1. Let l, k and t are both odd positive integers then for all B, a, a, b and c are…

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Q: 0.02x10.05x2 = -0.19 0.03x₁ +0.04x2 = 0.52 ○ X₁ = 5, X2 = 8. O x₁ = 7, 2₂ = 8 O x₁ = 8, 2 = 7 O x1 =…

A:

Q: -1 €С аnd z -1 -1 * If zeC /{0} then there exists z (х, у) # 0 such that z = 1. Let Z -1 Show that z…

A: The complex numbers follow two basic operations: Consider z1=a1, b1 and z2=a2, b2. 1.)  z1+z2=a1+a2,…

Q: Complete this proof in its proper format: Proof= { (∀x)(∀y)Rxy } |- (∀z)Raz Assumption:…

A: The given statement is ∀x∀yRxy|-∀zRaz. We have to prove this statement in the prescribed proof…

Q: 1. Using (2n +1)Pn= Pn+1-P-1: prove that P(x) = (2n-1) Pn-1(x) + (2n-5) Pn-2+(2n-9) Pn-3+.... - and…

A: Given : 2n+1Pn=Pn+1'-Pn-1' To Prove : (a) Pn'x=2n-1Pn-1x+2n-5Pn-2+2n-9Pn-3+ . . . . . .…

Q: 7 (V3 +4} = - = - 64 (V3+i) 2) Using de Moiver's formula prove that:

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Q: max  z =  x1 + 3x2 s.t.      x1 + 2x2 ≥ 6          2x1 +  x2 ≤ 8           x1, x2 ≥ 0 For the LP…

A: A LPP is written in standard form as  max (or min) z = c1x1 + c2x2 + · · ·+ cnxn subject to a11x1 +…

Q: 10. A fundamental set of solutions of x' = 3

A: Given,        x'=-21-13-343-12x

Q: 7. The equation x² + ax + b = 0, has two real roots a and B. Show that the iteration method (i) Xk-1…

A:

Q: 2+i3 Evaluate zdz along the following paths- 1+i2 (a) horizontally from 1+i2 to 2 + i2 then…

A: The objective is to slove the above questions.

Q: 6. Show that when ) < |z - 1| < 2, e - ( - 3) (2 - 1)(2 – 3) Complex Analysis n=0 (z-1)" 2+2 2(z-1)

A: We use Laurent series to prove given example.

Q: Consider the ODE system x' = A 3 with A = 4 1 + 3 a) Use the method of diagonalization to find eA.…

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Q: Example 19-2. If y = 2x³ – x² + 3x + 1, calculate the values of y corresponding i. %3D x = 0, 1, 1,…

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Q: 4. Prove Theorem 2.6.5.

A: Let p,q be any two distinct points on l. Let r be any point on l. Let m be the line containing p and…

Q: 4. Using Z(n)= Show that Z(ncos no) = (z-1) (z'+2)cos0-2z (2-2zcos0+1)

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Q: ner method ation 3 on x² +

A: Given function is, x3+x2+xe+2x-1=0

Q: 223+-5 -j Suppose z1 = 2+ j, 2 = 3- j2 and z3 = -+j Evaluate %3D 2-a+3-j

A: Substitute the given values of z1,  z2, z3 in the given expression and simplify.…

Q: 6 Maximize Fenoi Z = 2x1 – 6x2 subject to anole 3i X1 – x2 < 4 - -X1 + x2 < 4 X1 +x2 < 6 X1, X2 2 0

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Q: Please provide a well explained solution for the following.  what is the Gauss-Jordan elimination…

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Q: The th roots ofz=a+ bi whenk=0, 1, ..., n-1. take the form: 0+2n COS 0+2n +i sin O [cos(0+ 2kx) +i…

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Q: THEOREM 4.3. Let l, k are even and t is odd positive integers then for all B, a, a, b and c are…

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Q: i) verify that y1(x) is a solution. ii) Use reduction of order to find the general solution. iii)…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 2 4 1 find A-l by the cofactor r 2. If A =0 1 0 0 4 - 3 such websites.

A: Introduction: Step 1: compute the Matrix of Minors, Step 2: Convert it to the Matrix of Cofactors,…

Q: Find gcd(2,3+5i) in Z[i]

A:

Q: Rewrite -5sin(15x)-3cos(15x)  in the form Asin(Bx+C) where 0<c<2pi

A: Given data is: -5sin15x-3cos15x To write -5sin15x-3cos15x in the form of AsinBx+C

Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

A:

Q: 39. 3x1 - 2x2= -1 4x1 + Sa= 3 Answer: 40. -1 + Sx2=4 -- 3x2=1 41. 6x+ 12-0 Answer: 42, 2x-2r3-4 43.…

A: “Since you have posted a question with multiple parts, we will solve first three parts for you. To…

Q: Example 5.8. Solve du 0 0, ax2 at for (i) u(x, 0+) = f(x), (ii) u(0, t) = 0, t > 0, (iii) u(1,t) =…

A: To solve: ∂2u∂x2=∂u∂t, 0&lt;x&lt;1, t&gt;0 And, the boundary conditions are: ux,0+=fx, u0,t=0,…

Q: 2.3.12 Prove Lemma 2.3.10 (2). Only need to prove #2 0f Lemma 2.3.10. Lemma 2.3.10. Let a E R. 1. a…

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Q: TODlem 16. Find all solulons of the equation z- 5z +4 =0 1 and 4 -1,1,-2 and 2 o -1 and 1 -2 and 2 O…

A: The given fourth degree polynomial is converted into a quadratic equation by using the substitution…

Q: 3. Find a closed form for sn = i-1 (15 — 5і). Sn (3 – 8i). 4. Find a closed form for sn = i=1 Sn ||…

A: close form is given below

Q: 2 -1 2 3 0 1 5 1 -2 03 -2 -4 1 6 7. Check your answer in item 6 using Cofactor expansion. 1

A:

Q: ху' — Зу %3D 2x3

A:

Q: To find P(0 ≤ Z ≤ 1.37) using Appendix C-1, find the row containing ----  in the far left column.…

A: Given information- We have given- P(0 ≤ Z ≤ 1.37) We have to use Appendix C-1. We have to find the…

Q: Choose the correct answer below. O A. If three successive Newton approximations agree in their first…

A: To find how to decide when to terminate Newton's method.

Q: 2. Assume that x > -1. Prove that (1+ x)" >1+ nx for n = 0, 1, 2, .... %3D

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Q: S = {x2 − y2 ∈ N : x, y ∈ Z, x2 − y2 > 127}. Prove that S has a smallest element.

A: Given S={x2-y2∈N: x,y∈Z, x2-y2&gt;127} Theorem (Well ordering Principle) Every Nonempty subset of…

Q: 1 1. f(x) = x = 3 6. f(x) = x = 2 %3D 2 I - 3 1 2. f(x) = 1³ + 8 7. f(z)= x = -5 I = -2 x+2 I +5 23…

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Q: d/dx (xnJn(x))=xnJn-1(x)

A:

Q: az Find for z = e2z-y.

A: Given : z = e2x - y

Q: 2. Using the identity [1 2 1 [2 0 –1 1 2 -6 5 - -4 3 compute -6 5 [1 1 Hint: 2 -1 I2 1 2 -1

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Q: 2. The quantum states of a particle moving freely in a circle of radius r are described by Pn(0) =…

A: Answer is mentioned below for c and d

Q: A = 1 0 0 -1 -1 1 -1 0 1 -1 -1 -1 0 0 0 a. Compute Ax, || Ax||2, and ||*|| 2. b. Show that || A||2 ≥…

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Q: 2. (i) x²-12√/2 = 17 and (ii) y + y = 18√/3 1 a. Ifx-√√5=2 then find the value of x-- X b. From (1)…

A: A detailed solution is given below.

Q: 1. Gaussian elimination and LU decomposition fails when OA left digonal element is zero OA left…

A: If A is invertible, then it admits an LU  factorization if and only if all its leading principal…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.