F Given: ABCX is a O: DXFE is a C. Prove: ZB = LE X, D

Q: 6. Let the joint probability density function for (X, Y) be 1 = eY, -у f(x. y) 2 0 < y<∞, - y< x< y,…

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Q: tazt Find ECx)ECX?) ,ECX-X)? for tor the fullewing.probubilty distabudia - 20 30 3/10 1/2

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Q: 4R Q13:- If R = RR3 R+R2 Show that we we (R +R

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Q: answer as soon as possible

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Q: Given: I || m and s || t Prove: 22 E 215 di 1/2 5/6 3/4 7/8 9/10 11/12 15/16 13/14 all b and c tl d

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Q: QI: Prove that vM ror VM 2 s where r and s are the positive integers unless M # r .

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Q: Find the yalues of k for which he series conxer ges.

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Q: Given: P1: (A V B) ⇒ (CAD) P2: (D V E) ⇒F C: A ⇒ F Prove that P1, P2 - C.

A: Given: P1: A∨B⇒C∧DP2: D∨E⇒FC: A⇒FTo prove: P1, P2├C

Q: Find all the values of z: (hìnt: use tvalues of the discrirninant) 28 + 423 +8 = 0 O -1.366-j0.366ó…

A: We have,z6+4z3+8=0Let u=z3, u2=z6∴u2+4u+8=0u=-4±44-4(1)(8)2(1)u=-4±-162u=-2+2j, -2-2j

Q: O Find the Posifi ve value of * that işfie the egquation x-2X+ 452Bisection methed)

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Q: Use geometry to evaluate J JR (8 - 2y)dA, where R = [O,3 ] x [0,4].

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Q: 3.3. Let a, BEC. Prove that la + B2 + la – B|2 2(la|? + |B|?), and deduce that |a + Va? – B2|+ |la –…

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Q: O Fimd the that is boun ded between fe)= 2-x ond gla) = 4-x² ef Hhe regitn glo) = 4- x²

A: Toipc-Area under the curve

Q: IF ADEF AXY Z, then DF 2 XY,IF ADEF = AXYZ, then DF 2 XY. O True O False

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Q: 4 The cylinder shown below has a radius of 3 mches and a herght of 8 inches Which of the follow ing…

A: As we know that the expression for the volume of the cylinder is:   V=π(r)2h   Where;…

Q: 2 Find.all.se.cond.partial.devevatives:. f(x,y)In(3xi+5.y..b.ue sint C.Z-ytan x a..

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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: If given points D at (8,11) and F at (-2,1), determine DF. 136 20 O 2/5 O 10/2

A: The coordinate of point D is  x1,y1 = 8,11 The coordinate of point F is  x2,y2 = -2,1 To evaluate :…

Q: f. . Prove false by creating a counterexample: 9(AUB) C P(A) U P(B)

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Q: 3-Evaluate S Fdr where 2X Cisgiven by rT) = C 3+U-3t)jrék

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Q: if z 2- j5 and w =1+ j2. evaluate: 4- conj (z) - u 32 + j36 -32 +j36 36 j32 O-36 j32

A: Please check step 2 for the solution.!

Q: 9. The Pength of the Curve ņ = 206ti t2dintj ,0ts IT is :- (0)21 (6)47 (c) 87 (d) 1677

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Q: f Gx) =800,002 20+ 50eX Find fle inverse funcfion and esplean cohal it eans

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Q: d 20. a) dt b) Evaluate: + dt 1

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Q: ·/ / √₂ (²2² +2² (x² + y² + z²) dV, where E is the ball x² + y² + z² ≤ 16 Evaluate

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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: 9.m X implise that X,4x in صواب İhi

A: True

Q: What values of y and z make AIJK ≈ AQSR? I R y+17 y = Z = S Z+38 48 J 19 K Q

A: Given query is to find the value of y and z.

Q: ·[ [ [₂ (2² + y² + 2²) dV, where E' is the ball z² + y² + 2² ≤ 1 S Evaluate

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Q: Let C: |z – i| = 3 and I = $. e 5z dz. Then 22 %3D |= 4ti |=0 |= 6ti None of these |= 10ti

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Q: e3Z Let C: |z-il=3 and I = $. dz. Then z2 O I= 6i |= 8rti O None of these O I=0 O I= 4rti

A: Solved using cauchy integral formula