2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: -25 (1+j2 2-j5 ) = 57 + j24 2 \3+j4

A: We need to simplify the expression -2521+j23+j4-2-j5-j and show that it is equal to 57+j24 Consider,…

Q: 3) yo'ty"-2y=Dxe"* %3D

A: Given that y"'+y"-2y=xe^(-x)

Q: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

Q: f(x) = mx2 - 4x - 3m = m = ? A). 3 B) 5 4 C) - 3. D) - 2 8 E) 3.

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Q: Consider the following 3 x 3 matrix A and b in R, 1 -4 8 | A = 2 -3 2 1 5 -8 1

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Q: If A = (a, b) and B= (b, c), find: (i) (AUB) (ii) (AnB)' (ii) A'UB

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Q: a) Find ū - i b) Find w.u 1/2

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Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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

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Q: If r(x, y,z) = (x² + y² + z²)!/2, find a²f a²f əx²'əy² ' a²f , аnd дхду

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Q: Let G = (a, b | a² = b² = (ab)?). a. Express b²abab³ in the form b'a'. b. Express b'abab³a in the…

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Q: 2. y = Vg(h(x)) (g) cha))た. A'(x)'a 1,

A: To find the derivative y=√(g(h(x))

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Q: 1-3у 2у - Зу? 1.

A: Given: ∫1-3y2y-3y2dy

Q: A Find a numbel z That satisfies The condubion g af The MUT I dx= 9 4 -4 O -a 0-15

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Q: Let u= and v= identify 3u+v???

A: We have to identify 3u+v for the given vectors: u=2, -3 and v=4, -1. Finding 3u: 32, -3=6, -3

Q: P → (Q → R) is equivalent to A. (P ^ Q) → R B. (P v Q) → R  C. (P v Q) → ∼R D. None of these

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Q: Show validity: Vxр (х, f (x)). Vx3yp(x, y)

A: Please check the answer in next step

Q: d) fast!

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Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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Q: Suppose ū = (-4, 1) and ū = (0,4). Then: u+0= u - D= 0 - u= 4u= 4u – T0=

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Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c 3 1(1-x*) ? +E E

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Q: 니ut-4) (r-3'- 16 3')] = L. | %3D 8le ( (r-In 3) (r-In 3)2 ( * 2. 64e-3 (r-In 4) 6. (r-In 4)2 2 (-4)…

A: Lapalace transform satisfies linearity property, La·ft+b·gt=a·Lft+b·Lgt By laplace transform table…

Q: Which of the following is a contradiction? ○ ((P VQ) ⇒~ R) ^ (P^Q ^ R) O ((PVQ) ⇒~ R) ^ (Q⇒ (RV P))…

A: Definition:  A compound statement is said to be contradiction if it is false in all cases of…

Q: Just need help on (d), thank you!

A: It is given that the mean is 67 inches and the standard deviation is 2.5 inches.

Q: Which of the following is FALSE? O a. a. ((x →y)^x) →y O b. ((x vy)+(~x V ~y)) Oc. (x(xv y)) O d.…

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Q: O foxy) = senx + seny + Sen(xg) t1 %3D 2 fcxry) = xe y concet)t 8x

A: