12. Solue the morix equation for o,b,cond d 2 -37 12 34 こ

Q: dx , if we let u =V 25 – x² , then udu = - xdx. (A True B False

A: Given query is to find statement is true or false.

Q: · Find fF · dĩ for F = -yi – 4x j+4zk if C is the helix æ = cos t, y = sin t, z = t, for 0 < t < 47

A: Given F→=-yi→-4xj→+4zk→

Q: 2 sinºe cos³e de= 60 a O 120 b O 1 .c O 60 .d O 120

A: We have to solve given problem:

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: 0. gy c ube a losed Cont Conlainig he okigin it. Pycoue thal az 2.

A: I have used Cauchy integral formula

Q: dw when r= 3 and s = - ar 3 if w = (x+ y + z)“, x=r-s, y= cos (r + s), z= sin (r + s). Find

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Q: J sin³ycos ydy. Evaluate: cos y A cosy C 6 8 cosºy B cosoy +C 8 6 c) none of the given choices cosºy…

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Q: Find U from the differential equation and initial condition. I'm know the answer but I don't know…

A: To solve below initial value problem.

Q: Calculate fryr if Ar.y,z) = &r-9*y³-z³. OA foe =-322 OB fye =0 OC None of these OD fye = 3r2-3y2-322…

A: We have to find the partial differentiation of the function with respect to X y and z

Q: dz If z(x, y) = x²y, æ = 4, and y = u³ v², find du

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Q: 26. If RX = 6z+2, XS 18, and RS = 14z, find z. j %3D %3D

A: Recall: If XY is line given such that XZ=a ; ZY=b and XY=c then  XY=XZ+ZY   ⇒a+b=c   Note :…

Q: 6) Given that h(x,y) = e**y® _ ¥² Find hxx, hxy, hyy, hyx

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Q: 2 W = Span- - 1 1 .Then, the distance and y = 1 -3 -21 3 11 ny to W is

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Q: 12 Deter mine the hunchon fbc) 13 conhintdeus at loe Birked 1S Pes) Conhinaus at oc =0?

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Q: (b) Hạ: u < HO,n = 30, t = 2.431 = 0.011 P-value %3D

A: Given : Ha : u &lt; uo  n = 30  t = 2.431

Q: dz dz Find Ju when u = In 2, v=5. if z = 20 cot 'x, and x= e" + sin v. and dz (Simplify your…

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Q: 1) Let c. 12i| =3 and I = e dz. then %3D I= 1o TTi? %3D

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Q: (6) Euter eio_ el" = Cos e +i Sino, whore i = J1. where i= JT,

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Q: Convert the ! √ √4-1² 2 0 following to rectangular 32 r³z² sino cos o dz dv do dz dx dy

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: 4 - If w = x + 2y + z? , y = r2 + In(s), and z = 2r = X find at the point (r, s) = (-8,4). %3D

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Q: 2. Evaluate 22 - iz dz, where the contour C goes from z = 1 to z 2 to z = 2+ 3i.

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Q: a2u 1 du 1 a?u = 0, ar? r dr (r,0) = 0, u(r,t)= 0, 0 <rsland u(1,0) = 0 pour 0ses %3D

A: Given,                  ∂2u∂r2+1r∂u∂r+1r2∂2u∂θ2=0                             (1)with u(r,0)=0,…

Q: 4.2 ezt So 2(z – ni)3d%, with C : |z – 3i| = 1.

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Q: 1 ds where Cis given in the accompany- + y? + 1' 26. Evaluate ing figure. (0, 1) (1, 1) (0, 0) (1,0)

A: It is given that, ∫C1x2+y2+1ds   According to Curl theorem: ∫∇→×A→·da→=∮A→·dl→ Therefore, above…

Q: az az and du #6. Use the Chain Rule to determine given that av z = x sin (y? – x) x = 3u – v?, y =…

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Q: You hare shown that e jul dw or , erchenying w and t Jlw) = Use a chume of veriables to genenle…

A: Consider the given information: δ(t)=12π∫-ωωejωtdω                  ..(1) δ(ω)=12π∫-ωωejωtdt…

Q: 6.S ke ten the Cate given by Poiar eq dot;in )=v=2S16 %3D fb r=2+ Cos o and Campute the arer boundad…

A: We have to sketch the given Polar curve. And find the area bounded by Polar curve.

Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: To evaluate y-csc²(y³)cor²(y³)dy, we let u =cse (v³) A True B) False | csch2zdz =-In|csch2z –…

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Q: 2² dædydzB = {(æ, y, z) =E R° 0 < æ < 1,0 < y < 1,0 < : < x}

A: Given triple integral  ∭Bx2dxdydz, where B=x,y,z∈R3:0≤x≤1,0≤y≤1,0≤z≤x. We have to evaluate…

Q: Let C: |z – i| = 3 and I = $. e 5z dz. Then 22 %3D |= 4ti |=0 |= 6ti None of these |= 10ti

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Q: Q: Proue Itort It coso t isino cis4e It Coszo - i sino

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Q: Ex: Find and . fie 28. u = rs? In t; r = x², s = 4y + 1, t = xy³ %3D

A: ∂u∂x and ∂u∂y

Q: Solue the differeulial equalion dy +9-é^ Cosre zo yo) =0. 2. by csing milne's methad with h = 0.1.

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Q: Q2)f f is Cont then Ifl is cont. IS

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Q: 10 Compute r''(t) when r(t) = (tº,3t, cos r'(t) = %3D

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: -41 sin tZ dz, c: 1Z-il=2 z4 ans: 3. coshz dz ,C: IZ1=1 27T ans :

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Q: a the diagram, PU||QT, Ì = 42°, RQS = 82°, = v, UPT =r and QPT = x+40°. Prove that PT|QS. %3D P…

A: Given: PU||QT Concept: Pair of interior angles on the same side of the transversal are supplementary

Q: S0scies 1CAR is inscribedin a E = 130°. %3D Finc: 12. iaCR 13. RC 14. mÃC 15. mAR

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Q: where: %3D Solue ulX, o)=2 X •a u (0,t)=o 1 ノ

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Q: Find C if r(t) = ⟨et, 3 cos t, t + 10⟩ + C and r(0) = ⟨0, 0, 0⟩.

A: We have given function r(t)   r(t) = ⟨et, 3 cos t, t+10⟩ +C   We have to find the value of C   It…

Q: 2- Evaluite the Value of 4he next nteg Pation by using Ahe trapezodal rule ; Then Find the absoluto…

A: Given the integral                                   The trapezoid formula is given by where…

Q: 24.)Graple the golur equation r=1-coae for'e in [0,360) 30 45 60° use the brapl on the next page…

A: Consider the polar equation

Q: Ⓒ'Evaluate Sot So Sox sing ²sin y dy dz dx tim of the

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Q: 17. f (1,y, z) = x subject to z? + y? + 2² – z = 1 %3D

A: Let h(x, y, z)=x2+y2+z2-z. We now have ∇f(x, y, z)=(1, 0, 0) and ∇h(x, y, z)=(2x, 2y, 2z-1). Let λ…

Q: Let be Z= ax? yf +bx²y³ 9 and b que cors P is a pant givon by (-1,-1) qnd we Anaw dz (P) = -2 , &르…

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Q: cos(2) dz c (z – n)(z – 27)3' 7. Evaluate where C : z– 27 = 27 described once in the clockwise…

A: Q7 asked and answered.