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

Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: 5. If u = e1#1+az#2++anIn, where a² + a³ + · ·..+ a = 1, show %3D + = U dx?

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Q: Aşağıdakilerden hangisi R° için verilen S bazından üretilen ortonormal bir kümedir? S = 3 -5 Lütfen…

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Q: Given: z = x3 + xy", æ = uv + w°, y = u + ve" az when u = 3, v = – 2, w = 0 Find

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Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: 4. Given that T : R² → R* and is defined as T(x, y) = (x + a, y + b) . Prove that

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Q: In(u cos v) and y = usin v. Evaluate and z at the point 2е" In y, x 3D (u, v) = (2, 7/4). Let z = du…

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Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: Let z = ety, where x = Vuv and y . Find dz in terms of u and v.

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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: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

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Q: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: Calculate ∫c (2 + z) ds, where Basket given by r (t) = 4/3t3/2i+1/2t2j+tk, 0≤t≤1

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Q: Aet statyested that PON fghle v wi the nest presintenS 0 v e rand ptaton of a e voen probatity tha…

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Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

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Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: 63. r(и, v) %3D Зи сos vi + Зи sin vj + 18u'k ||

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Q: af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

A: Given problem:-

Q: 5={cj+ kn, u +vn): nez T={(x,y)EZ:157 x +107 y =- 157 x +107y=1 choose j,K, u,v EZ, such that S=T"…

A: Linear Diophantine equation: A linear Diophantine equation in two variables takes the form of…

Q: (i) Evaluate S(z + 5i) dz where the path is the line From z = 1 to z = 2 +i

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Q: In Exercises 53-58, compute the derivatives indicated.

A: Here given as fx, y=3x2y-6xy4 Now ∂f∂x=∂∂x3x2y-6xy4=6xy-6y4∂2f∂x2=∂∂x6xy-6y4⇒∂2f∂x2=6y

Q: Given: y2, = uv4 + w*, y = u + ve"| z Find when u 1, v = 3, w = 0

A: We know:

Q: ) ind the standard matux Der the stated in Re 2Anylection about the linn yez Golleued ya 60°c.…

A: We'll answer the first question since the exact one wasn't  specified. Please submit a new question…

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: Consider the formula A = Vx Vy.p(x,y) ^ ¬q(x, y). (b) Show that A is falsifiable (i.e. not valid) by…

A: We are given a formula as : A≡∀x∀y.p(x,y)∧¬q(x,y) We need to show that A is falsifiable by giving an…

Q: O The madices of cervadere af r= éat any poind Y, is (@) r?VTt (b) rvite? (C) Vitaž (d)

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Q: O Given the initicl bouridary conditions y(0) =0, y'c0) = 1, letrmine the, solntiem of %3D…

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Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

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Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: Let X - Y (3, 0.02). Given Ttx = 300 calculated by the Esscher Premium Principl %3D

A: From the given information, X~γ3, 0.02 fx=0.023γ3e-0.02xx3-1, x>0       =0.000004e-0.02xx2,…

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: 13 ABCD is a trapecium with ABDC. A line parallel to AC intersects AB at X at Y Prove that ar…

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: Use Green's theorem to evaluate s cy? oy)dx + (y²rlo4") dy where Cis s hoon belbw, N y = 2-x² G,1)

A: The given path contains 4 curves: C1:  from (1, 1)  to  (-1, 1)C2:  from (-1, 1)  to  (-1, -2)C3:…

Q: Be u = x2 + yz, where x = rsin(t), y = rcos(t) and z = rsin2(t), calculate: ∂u/∂r and ∂u/∂t

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Q: let A and B be matiices of Con det A) = -1 find the Valué of Cdet(z AT) - dct(-2B )) LA Pproxi mate…

A: Given:- det(A) =-1/2   ,  det(B) =2/3 To find:- [det(AT/5) -det(-2B-1)]2

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: - a. ARWZ W WZ RW b. ? ZR %3D c. RW = 15, ZR = 10, and SZ = 8. WZ 2 and RS = ? R

A: Given, ∠WRZ=∠WZS

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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

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Q: (R, d), where d(r, y) = |r – y|, is separable. %3D

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Q: dv E={my,)|→<y<4Y<そく4, Osns? そ

A: Given that  Triple integral of z/(x^2+z^2) To evaluate the integral

Q: az au əz əv əz ?w 11 11 || z = x² + xy³, əz əz du av az aw x = uv³ + w², y = u + vew when u = 1, V =…

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Q: me succe LO SUIVE uie folnoWing 2 и (х)— | (x -t )u (t )dt 2 --

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Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: f(z, y) – zsiny +e, then Vf(r, y) (0, e").

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Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.