Let f(z) = ((z – 31) + 9)ez-. Evaluate fe f(2)dz, where C is Iz – 2i| = 2, positively directed. a) 0 b) ni c) 9ni d) ni а. b. C. d.

Q: p) Classify the following models as ARIMA(p,d,q). i) (1-B)x, = (1-0.3B),. ii) (1-0.5B+0.25B²)Vx, =…

A: ARIMA means auto regressive integrated moving average, It ia also written in the forn ARIMA(p,d,q)

Q: 1 Let f(z) = ((z -3i)² + 9)ez-3¹. Evaluate f f(z)dz, where C is |z − 2i| = 2, positively directed.…

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Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: How, Form P.D.E. from: a (3) Ucx,y) = (x²+a)lytb)

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Q: Let C z-1=3 and1 = §, = dz. Then

A: The solution is given as

Q: c) Find u (v x w) if u = [0,0, p], v = [0, q, 0] and w = [r,0,0]. %3D

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Q: 3. Which function has a range of yS 3? Ax) -- +3 с. a.

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Q: Let (a, b) = 1. Prove (a2, b2) = 1.

A: Let (a, b) = 1. Prove (a2, b2) = 1. Given (a , b) = 1. Which means a is relatively prime to b

Q: d²y| -x² + y² – xy + 1 = 0 — ху + 1 3 0 dx² (1,1) 12 - O A) 3 O B) -10 о с) 10 D) not fne E none

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Q: Determine C if u=v=0 (20 — 5и + 3)dv — (20 + 4и — 6)du 3 0 - 3 27 -1

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Q: Let f(z) = ((z – 3i)² + 9)ez-, Evaluate S. f(2)dz, where C is |z – 2i| = 2, positively directed. a)…

A: Given that fz=z−3i2+9e1z−3i. We have to evaluate ∫Cfzdz, where C is z−2i=2. Use formula:-…

Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: 3. Let R= {(x, y) : x² + y² 0, y > 0}. Evaluate // Vz? + y² dA x2 +y? dA R

A: using polar coordinates x=rcos(θ)y=rsin(θ)x2+y2=r2,dA=r drdθ

Q: (1) Let F =x?++zÂ, and let u= ||FlI. Let fcu) = 3ue 2-2u Show thet Df(u)= 6-6u)eu F -2u

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Q: 2y 7. 3. Evaluate ST (r+y)dx dy. 32 A) 3 64 C) 3 16 B) 32 D) 3

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Q: Let u= 31-2j + k and v= 2i – 2j + 2k. Find ux y.

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Q: Hx.y)=Vtanlx)+y and u is the wit etor in the direction find U IS 6)DE(-04,7) - a.d,7)=Dy F(-a.l,7)=…

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Q: Creani Cet G4)= ti t2+34)j +4k HICH) = 2JF L+3tj + find a) H4) XG4) (1+24)k こ b) G4). HGE)

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Q: u = [-5, –1] v = [9, –7) w = [8, 1] 5u + v – w = [ Ex: 6

A: We will use the co-ordinate wise vector addition definition in R² where, u, v, w are vectors in the…

Q: Let A(0, 1) and B(1, 3). Find the point C such that 0 (24) (2-4) (-2,-4) O (2.5) O(-2-3) AC = 2AB.

A: given   A(0,1) B(1,3) let  C=(x,y)

Q: Prove that a. V. (A + B) = V.A + V.B b. V. (ØA) = (V. Ø). A + Ø(V. A)

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Q: Let Fi x?+y",x= v u², and y= v df du Find A.) 5ytv-2ux B.) 5yY -2ux (-) 2x +Fy? 0.) (2자 +5y)(v-u E.)…

A: See attached file for a step by step explanation to find the required partial derivative.

Q: 5. If 3x? +2xy + y? = 1, then y' %3D 1-3x-y c.) d.) - 3x 3x+y y? 3x+y a.) b.) x+y x+y 1+y 6.…

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Q: Determine f (t), if F(S) is equal to: 6s? + s - 4 s(s – 1)(s + 2)

A: The given function F(s)=6s2+s-4s(s-1)(s+2)

Q: Q4: Show that: Hint: use the following: 00 S 8 sin αω. αω -)² dw = RIO T a F[u(t + a)-u(ta)] = 2a…

A: To Show- Show that: ∫-∞∞sinaωaω2 dω = πa