Z1 and 22 are complementary Z3 and Z1 are complementary ВС | DE Given: Prove: A 1 3 D E

Q: Q(3): Show that: (a) Vx Vo(r) = 0, and (b) V-VX E(F) = 0.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: 1 Prove that 3 dx s VI VI

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Q: (6 y x - 2 y)d A R=[1, 4]×[0,3] 9 .A O 9 2 .B O 2 9.

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Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

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Q: Verify that and use this equation to evaluate 2-1(2-4) (Aª dx 1

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Q: Prove the product rule by use of ΔA=w⋅Δh+h⋅Δw+Δw⋅Δh

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Q: Let G = (Zj0, X10) then o(G) is а. 5 O b. 4 С. 3 O d. 2 О е. 10

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Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: [2 1] Q2) Assume A = |1 3 L3 4] [2 4 6 4] ㅋ 4 and B = 13 show that (AB)' = B' A'

A: Solution: The objective is to show that the given relation

Q: = Y, = 1 + + x2 2 → 님s = 1 + +x? dz → Y, = 1 + 24 4 1 → Ys = 1 + 와 24 3

A: We have to find out

Q: If z = (1+ iv3)' 100 then find the value of Re(z)/Im(z). a. V3 b. 1/V3 с. 2//3 d. -V3

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Q: Prove from the definition: n3 + 65n2 + √n = Θ(n3)

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Q: Given u = -6i + 6j + 6k and w = -2i + 3j + k. Find Ju – w| V50 None of these 4

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Q: 3. 1+-=. 1. х*— 13х2 + 36 %3D 0 2. ха — хе -2%3D 0 3 3. 2n 2 n2

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Q: Let gcd(a, b) = d then which of the following is correct (i) (ii) b|d (iii) d|(ax – by) v[p a. All…

A: gcd(a,b) = d  So, by definition, d | a and, d | b  &, d | (ax - by) for all integers x & y…

Q: 13 = 523411:KER 3is a sbuet 2x+1 wheher Bis 3 If B Decide t so is asbet of TR aboveand bounded find…

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Q: [S (x2 - Dx + 17) dx, = 7. (40.5) о The base b is: а) 20 b)22 с) 21 d) 23

A: First you have to know how to calculate base  Fisrt find D  then use the formula b = D * upper limit…

Q: Q1: z = e*/y find дх

A: Let's find.

Q: Prove that bx q = b. ((Vt) - Vt), where q = V x t

A: We have to prove b→×q→=b→·∇t→Tr-∇t→ for q→=∇×t→ b→×q→=b→×∇×t→          =b→×∑i^∂∂ti×t→…

Q: Evaluate dx V In(8-x)) at x = 1. = 1.

A: We have to find: ddxln(8-x2)3   at x = 1.

Q: 2x A In 9

A: here option D is true

Q: 29 – 49 - dy C. 2+ 4y · Evaluate using substitution

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Q: Given R = a) b) 24 15 and S = 2STR 5R+S-(2STR)T 1 3 15 Find

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Q: Calculate the convolution: x * 2 * e2* . x2 e2a O a. 4 4 8 e2a Ob. 4 4 8 - 4 2 4 O d. 1 x2 e2æ 4 2 4…

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Q: Let a,b E R with a # 0, b # 0. Prove that (ab)¯1 = a°1b´1. %3D

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Q: 2 A=[²2 1 4] IF A= 2 and B= 3 2 L3 4 31 1 2] Find AB :

A: Matrix multiplication is always done from each row to each column, i.e., row to column…

Q: Evaluate – 3j + 4a – 6 + f' when j = 9, a = – 7, and f = 7. - Question Help: O Message instructor

A: We have to find out

Q: Evaluate V3 dx 1+x2

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Q: Find B so that BH B = A where A is from (1).

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Q: || 16xy dA 76. RJ E (и + v) 4 1 y : - и) ||

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Q: 123 A=162 3 3 5 9 3 Let Calceelate Ā By Cayley- Hamil ton theorem.

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Q: Find (1 + i)' and P.V. (1+ i)'.

A: Principle value of the number of the form ab, where a,b∈ℂ-{0,1} is given by: P.V.(ab)=ebLoga Let z…