(B) Evaluate: [7zdv 72dV, where E= = {(x, y, z) |0 ≤ y ≤ 2,0 ≤x≤ (4-y²),0 ≤ z≤y}.

Q: 22² +52 + 14 (2-1) ¹ If U(z) = CSScanned with CamScanner 9 evaluate u₂ and uz

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Q: prove if x → y then xor y = y =

A: To prove : If x→y then x or y = y Lets use the help of truth table to prove the above statement.

Q: Evaluate (Vx+ f. d dx. OA. A. Vx2 + 2 + a² - a In + C O B. Vx2 + a² - In |x| C. Vx2 • a? + In- + C…

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Q: If 9 = {(1, y) |1 ≤ x ≤ 3,3 ≤ y ≤ 6}: D then: 11,3 dr dy

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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: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

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Q: S(x)dt, iff(x)= Vx-k+1;k-13x< i, k=1, 2.n.

A: By substitution, we calculate the following Integral.

Q: Determine the global extreme values of the f(x, y) = 9x - 4y if y ≥ x - 5, y ≥ -x - 5, y ≤ 7. (Use…

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Q: Linerije he lien apantion: 1. yeation; nen- x* xy+ 3y sie the ryin *T/ テ

A: Solution: We have to linearize the equation z=x2+xy+3y2 within the region 2≤x≤3,  11≤y≤12 Let us…

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Q: Given that P(X)= P(Y)= and P(XUY)= find 20 20 10 a) P(XnY) b) P(XIY)

A: Given,PX=920PY=720and PX∪Y=710

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Q: Evaluate Va? + y? dA where R= {(x, y)|1< x² + y² < 4}. 4.

A: We will convert this into polar coordinate so it will easy to calculate this We consider…

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A: Given f(x,y)=x2+2yy2-x. The main objective is to determine fx.

Q: so be it r = 3xi + yi – 2zk and f (r) = –- where r| = find all of grad(f) and div ()

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Q: Consider the following statements, where the domain of each variable is R: (1) Vxy ((x+y=2) ^ (2x -…

A: True or false

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: a(k) = eak coshw.k coshw, k ewok te-wok 2 eak coshw.k eak ewokteake-wok 2 X(Z) 3D글 z(enk e.k) + 글…

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Q: Which of the following is equivalent to (p → q) A (q → r) → (p → r} None O True (q→r) A (pq) False

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Q: Suppose U = R. let p(x) : x 2 − 2x − 15 < 17, then the statement u : ∃p(x) is (true or false).

A:

Q: 1. Translate these statements into English, where the do- main for each variable consists of all…

A: a) for all x, there exists y such that x is less than y b) for all x, for all y if (x is greater…

Q: 5. Prove that if x, y ER, then x + y ≤ x + y. Use the following cases: (i.) x, y ≥ 0, (ii.) x, y <…

A: We now prove that if x,y ∈ ℝ , then x+ y≤ x+y with the help of given three cases.

Q: If X, Y, Z ER and x≤Z, show that XL Y S z if and only if |x-y| + | y-z| = |x-z). Interpret…

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Q: Let z = 6ex²y³. Then: дz дх дz ду

A: We can solve this as follows:

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

A:

Q: Q: Let z = -4 V3 – 4 i %3D A/ Find the following : 1) Iz| 2) arg (z)

A: Since you have posted multiple questions but according guidelines, we will solve first question for…

Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

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Q: 7. ) Let f: N→ Z with f(n)=n+4. Let A = {1,2,3} and B = {1 € Z \ I <10). Use these to find the…

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Q: Evaluate f (x + y − z)² dV for the box B with dimension: [0, 6] × [0, 4] × [0, 3]. (Use symbolic…

A: Solution :-

Q: Let f(x, y) = x for y=0 and 0 for y+0. Evaluate each of the following or if they do not exist, state…

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Q: 1 s) Let f(x, y) = x¹y-²-5ry- ? (graye ! 'e' e7 In (2ry), find fzz, fyy, fry, and fyz. Sadda

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Q: Given f„(x, y) = cx (x - y), 0 < x < 2, – x <, y <.x, and 0 elsewhere, (a) evaluate c, (b) find…

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Q: Find: ii) P (X₂ ≤ 1X₂ ≤). f(x₁,x₂) = {1x1x² 0≤x≤1, 0≤ x₂ ≤ 1 elsewhere

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Q: H.W. a PDE from the followi'ng- @u=f() Form メツ 0u=fcx?ー)

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Q: Prove by direct method: if x, y>0  such that x ≤ y then √x≤√y

A: