The property S (2, y) drdy = S Saf (x, y) dydx is true according to the theorem of O None of these O Cassini O Fubini O Lubini

Q: If x* + y* – xy+z – 3z = 1, then dz %3D a) None of these b)금 (423-y) c) y-4x3-4y3+x 2z-3 d) y-4x3…

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Q: Assuming that two Customers, A and B, at a lawyer's are due.to ot. arrive Office during the same…

A: We will be using geometrical probability for this problem. Let x denote the time spent after 10:00…

Q: construct an FOL proof for ⊤ ⊢ ∀y(y=b → P(y)) → P(b). ⊤ means there are no premises and ∀y(y=b →…

A: The objective of the question is to construct a First Order Logic (FOL) proof for the given…

Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

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Q: Q1) prove the following below i). Corr(X , Y ) ∈ [−, 1, 1] ii) E(X|Y) = E(X) or E(Y|X) = E(Y) ⇒…

A: We need to use the concepts of Variance, Covariance and Expectations to solve given question.

Q: 3{x.y.2) : x+y²+z's 1024, z2 o}. Let D= Evaluate z dv.

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Q: Evaluate (2z + z – i) dz J|z-il=1

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Q: ο(*) *fx- | ii) fx+nn = Σ=o

A: As per the question we have to prove the indentity relating the forward difference ∆ with the…

Q: Prae that x– )is boundol incleasing saquence di numbers, then X is Convergent and lima>alxn) = prove…

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Q: If z = 3x2 – 2y3, x = 1+ s²t and y = 33 – t2, then dz %3D O a) 6x(1+ s²)+ 12ty O b) 6s²x – 12ty - c)…

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Q: H.w 3: Apply the Trapezoidal rule to evaluate SiSit 2xydxdy (1+x²)(1+y²)' taking h = k = 0.25. 110 +…

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Q: 1 e x² + y² + 2² dv₁ v ¡dV, where E = {(x, y, z) | 1 ≤ x² + y² + z² ≤ 4}. 6. Evaluate

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Q: - Z Let h(x, y, z) Then 3 (x² + y2 + z²) 2 ah А. (x, y, z) В. (x, y, z) = ', Y, dydz C. As a…

A: Here is the solution

Q: OProve that (r=s)Er S is toutology?

A: The objective is to prove that r≡S≡r↔S is a tautology.

Q: dz; |z – i| = 1 (z – i)3

A: We have to use the Cauchy integral formula to evaluate the following integral ∮ ez2z-ι3dz over the…

Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

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Q: re 'C' is z-

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Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: Tove or disprove the following claims. et W, X, Y, ZCZ a) (W-X)- (Y – Z) = (W –Y)-(X-Z)

A: To Prove or Disporove (W-X)-(Y-Z)=(W-Y)-(X-Z)

Q: 3 3 fx J,cx) dx = (x-4x)J, CX) +2x J,cx)+c (x-4x)J, CX) +2x JoCX) +c

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Q: Let a,be Z-{0}. Then one of the following statements is false A)lf ax+by=1 with x,y eZ, then…

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Q: c) If f(x, y)= e" cos 2x, then show that = 0.

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Q: if x, y>o such that x Sy then Vã svy Prove by direct method

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Q: Ex let x be with pmf 1=,2,3, 16 O find c P(X)2)

A: We want to find the value of c and P(X≥2) and P(X2=9)= ?

Q: m!n! If m, n e N, then prove that ,, dx = m.n (m+n+1)!

A: A detailed solution is given below.

Q: Prove that (S ⋂ T)c = Sc ⋃ Tc and  (S  ⋃ T)c = Sc ⋂ Tc .

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Q: u = 3, o2 = 9, P(-6 < X<12) a. Determine P(u – ko < X<u+ ko) 1 - 1/k?

A: According to the Chebyshev's theorem, 1-(1/k²) of the observation fall within k standard deviation…

Q: tr(AA') = (tr(A))* There exist square matrices A and B such that AB-BA=I.

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Q: 4z2+4 Let C: z+1=4 and I = = §. dz. Then z2-1 |=-2ni 1=0 (without applying Cauchy-Goursat Theorem)…

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Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: O If z-frxy) show that つる

A: As per our guidelines we are supposed to answer only one question. For the solution of the problem…

Q: 49. Differentiate y = cosh²4x a. 4(sinh 8x) b. 12(sinh 8x) c. 8(sinh 8x) d. 2(sinh 4x)

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Q: 4 GuNeer that K 9 laJ ) ficed fle xale of K 2 5,

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