QUESTION 13 (z – 2i ) (z – 3) Given f (z) = %3D z² (z+5)³ (z -2i) 4 3 Which of the following is correct ? o z = 2i is a pole of order 3 oz = 2i is a pole of order 4 z = 0 is a pole of order 3 oz=5 is a pole of order 3

Q: QUESTION 9 dz (1+4r) dr – z?, for z (0) =4- Find the solution z(r) of: O a. none of the above 4 O…

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Q: The roots of the characteristic equation of (D2 – D+ Dy are A1 = 3 + 4i and A2 = 3 - 4i . 25 15 10 4…

A: We will find the value of the unknowns.

Q: Question 2. If f(x) =x² + (a – 2)x+2-a then f(x) has a repeated root at x = 2. Find the value of…

A: The objective is  to  to find the value of a

Q: Question 9 If X = /1 - t and y = t 3 - 2 t what is y'when t = -1? A) - 2 2 B 2 V2 2 D

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Q: QUESTION 2 Let g(x,y,2) = xyz? - ysinx Find vg(n,1, - 2)- Oa (3,4n, - 4 r) Ob3 OC (5,4n, - 4n Od.5.…

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Q: Yt = Y(t-1) + e(t) - .1 e(t-1) Which ARIMA model is this? (Identify p, d, and q.) What are the…

A: ARIMA model is given as  :It is denoted as ARIMA(p,q,d)where ,p represents the autoregressive…

Q: Question 1 Let f (x, z) 4xz - 2x + and g(x, z) = 3x-z+ 2xz - 6. %D Find: af(x,2) blank 1: дх…

A: f(x,z)=4xz3-2x+1z,   g(x,z)=3x-z+2xz-6

Q: 3. Let A = 20 A AB 9. (a) Find, (b) Find, (c) Find, 730

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Q: 1 1113 D.9. Let A=3 4 3 0 0 Then (a) Find the bases for Col A. ROWA and Nul A. (b) Find the rank and…

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Q: Question 6 Compute comPpa given a = (2,0,- 2) andb=(0,-3,4>. %3D

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Q: 2. Let f(x, y) = x³y + y² - 3xy. In which direction is f increasing fastest from (a) (1, 1) and from…

A: We have a real valued function of two independent variables. Such a function is called a potential…

Q: (D² – 2D + 5)y = e* cos x

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Q: Construct the fundamertal soluton G(x, E) -?G= S(x- E) X, E ER? with, as x -E00 or

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Q: [2 1] 6. Given that, P=|-1 3 Q= [-2 2] [2 1] [3 -27 and R= 0 3 4 a) Show that (PQ)F = Q° P* b) Find…

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Q: Question 5 (D2 - 3D + 2)y=e5x, Find Y = Yc + Yp 1 2x + a. O b. O C. Cet + C с d. ce -X e 2 + C₂ e…

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Q: 3.6 Given flxy) =Sinx+y) where X=St,y-3s-6t find falx(s,t), yls,t)) %3D and filklGst),yls;t))

A: Given, fx, y = sinx+yx = s3t6y = 3s-6t Find: fsx, yftx, y Used formulas, ddxsinx = cosxddxxn =…

Q: 1.3 Evaluates 2y³ ev. ey²(y² – 1) + C а. b. -ev (y² + 2) + C С. 2ev* (y² + 1) + C d. evy + 2) + C

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Q: Evaluate I = fc (sin(x) + 4y) dx + (9x + 7y) dy for the nonclosed path ABCD in the figure.

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Q: [1 -4 -5 -4 3 T:R* → R° is given by T(7) = Ai where A 2 -6 Find all a in R so that SO 6. -4 T(교) %3D…

A: We have to find all the x such that T(x) = 0:

Q: – 10x J (2x – 3)(x + 5) 11 - - Evaluate + C

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Q: Question #5: Drive the following (write all the solution steps): 1. VxVU, where U = F (x, y, z) 2.…

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Q: -5 2 -3 In R° let z = 3 X = x= -1 and y = 2 6. 4 . Write z as a linear combination of x and y.…

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Q: The function u (x, y) = x² – y² – y. Find its conjugate v(x,y) if possible. O None of the above O…

A: The function u(x,y)=x2-y2-y has a conjugate if it is harmonic. Here,  uxx=2x,uyy=-2because…

Q: S[e?+*+ysinw)]ax +[ev"+ 2xcos(y)lay. Let C be the rectangle with vertices (0,0). (2,0), (0,1) and…

A: This line integral can be solved by Green's theorem as explained in the steps below.

Q: 10(8x13 + 7)° + 13 Set H(x) = and g(x) = 8x13 + 7. Find f(æ) such that H(x) = (ƒ o g)(x). %3D 8(8213…

A: f o g(x) means g(x) function is in f(x) function. Example:- Let , f(x) = x2 + 3x + 1  and  g(x) = 2x…

Q: Let V = R² and S = {(x, y) = R|x + y = 0}. If v = (1, 1), then what is the coset v + S. The line…

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Q: QUESTION 15 (z – 2i) (z –3) Given f (z) = ? (z+5)3 (2-2i)4 Which of the following is correct ? O z =…

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Q: The stem-and-leaf plot shows the test scores of a science class. How many students scored 75?…

A: Here we have to identify from given stem-leaf plot how many students scored 75

Q: QUESTION 9 in = where z = g(u, v) and u(r, s), v(r, s). Find the number of terms in

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Q: If A = x° yz? î – 3x² z³ j + yz? k , then a² A at the point (1,0, 1) will be дхду 3 î -3) -3 î

A: The vector A is A=x3yz2i-3x2z3j+yz2k find ∂A∂y=x3z2i+z2k ∂2A∂x∂y=3x2z3i the point 1,0,1…

Q: -4z2-4 Let C: z-1|=3 and I = 4, dz. Then z2-1 O None of these O I-0 (without applying Cauchy-Goursat…

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Q: (z-2i) (z – 3) Given f (z) =- %3D z² (z +5)3 (z–2i)4 Which of the following is correct ? z = 0 is a…

A: Option (d) is correct At z=2i is a pole of order 3

Q: Differentiate In(3x4 +7x²+3) e 2x ³ +7x

A: The given function is .The aim is to differentiate the given function.

Q: ppose z = f (x, y), where x = rs and y =r+s. Find zZrs in terms of fæ, fæx, fæy, and fyy.

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.