When u × v = 0 and u ∙ v = 0, what can you conclude about u and v?

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

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Q: | 21×VX2 + 1 dx = 14 2- 7, what is 21uV u2 + 1 du? Given that %3D

A: The properties of definite integral is ∫abf(x)dx=-∫baf(x)dx. Use the property of definite integral…

Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

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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: How do you compute the magnitude of v = (V1, V2)?

A: Magnitude of v = < v1, v2 > Magnitude of vector v is represented as || v ||.

Q: Find (au / ay) at the point (u,v) = (√6, − 1), if x = u² + v² and y= uv. ди (2) (Simplify your…

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Q: aw Find ду if w = z³(In(zy))(e**y*z*) %3D

A: Given,        w=z3ln(zy)ex2y3z4

Q: Ut + 4tuz – 2u e', x E R, t > 0 u(x, 0) xe- , x E R. Find u(x, 1).

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Q: If WZ = 68 and UV = 94, what is XY? %3D V W Y U Z

A: Given ,  WZ = 68 , UV = 94  We have to find XY

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: Find (au/ay), at the point (u,v) =(√2,3), if x = u² + v² and y= uv. ди (2) = (Simplify your answer.)…

A: Given query is to find indicated partial derivative.

Q: 2. S → (T → U) U → -U (V → S) ^ (W → T) .. V → ~W

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Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: x then ux is XX If u = V y %3D

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Q: Prove or disprove: Vx € Q, Vy e Q, 3z E Q, (x < y) → (x < z< y).

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Q: Let X and Y be iid N(1,3). Let U = 4X + Y and V V_dependent or independent? Justify your answer. 2X…

A: Given X  and Y be iid with N(1,3). Mean, μ=1 Standard deviation, σ=3  U = 4X + Y and V = 2X — 3Y

Q: J 2+2 cot (2²+42 - 3) -dz

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Q: For the error term u, assuming that E[u] = 0 implies E[u|X] = 0 and vice versa. %3D

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

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Q: Prove that : V.(V×A)=0

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Q: 10. What is 2ri 2 fo, h (z) dz?

A: curve C3 encloses points of singularity z=-2 and z=0 in clockwise and counterclockwise directions.…

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

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Q: If v equals u +at.Find t when v equals to 18,u equals 9,a equals 2?

A: The given equation is v=u+at. To find the value of t, we have to substitute values of other…

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

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

Q: Find SV. T. 15 30 R U 16 V SV %3D Submit

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Q: (a) Explain the difference between Eai and Σα i=1 j%3D1 (b) Explain the difference between E a, and…

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Q: Ex. Show that V1 = 3i + 7j & V2 =i++1)j a %3D %3D are equal ?

A: Simple vector problem...

Q: 8. % = () Given that u = and w = calculate the values of x and y if 2u = v - w. %3D

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Q: im(z,v) →(0,0) F(x, y).

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Q: prove. that s U. W V- W 1. U.r V.r

A: Using the vector triple product, it can be written that: a→×b→×c→=a→·c→b→-b→·c→a→. Using the scalar…

Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

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

A: Change the z in the terms of u and v and the differentiate.

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

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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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Q: - show that; L-1[e¬v$] = e %3D 2tynt

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Q: Bef(u, v) = uv and v calculae %3D + vu- dvðu?

A: To find- Be fu, v = uv and v calculate u∂3f∂u3 + vu∂3f∂v ∂u2.

Q: If F (x, y, z) = xyzî – e² cos xĵ + xy² z³k, what is V · (V×F) (1, 2, 3) 1 2

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Q: ux v of u = 2i + 3j, v = -i + j is *

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Q: 2- SSi dA A A-{(,3):x7, ソプ andy=x, xy=6,火=8 14.4)' %3D Ans (448) Az ーに

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Q: a(x, y) r = u? -v,y =ue". Compute ô(v,u)

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Q: f(x, y) = e&z– 4y af af ду

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Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: Find he value of ds/du at u = 2 if s t2 + 5t and t = (u? + 2u)

A: ds/du=9/2

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

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Q: Find vf(x, y) if f(x,y) = e* c cos y 5.

A: Note : according to our guidelines we can answer only first question because there are multiple…

Q: [D] Evaluate det (A), where 0 0 a u b 0 A = v w с 0 2 d

A: Let's find.

Q: O eiz dz < z2 – i e2 , 3 - z(t) = 2e", t e [0,27]. true False

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Q: If f(2) = sin(z?) = U(x, y) + iV (x, y), determine U and V. Verify that the C-R

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Q: Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

A: Answer