IF X₁, X₂₁.... X n then show that is a rs from NC₁, 6²) U = {² (x²-1) ² ~ X ²nt 2 NO.: DATE:

Q: Write the following equation in index form V(div v)+u x (vxw)=p(c®b)a VX W

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Q: Autism and Maternal Antidepressant Use A recent study41 compared 298 children with Autism Spectrum…

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Q: 2. Determine the power set p(A) = {{a, b}, {c}, {d, e, f}} 3. Suppose A = [7, e,0} and B = (0,1}.…

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Q: 10 Sx³ex¹⁰dx= (Type an exact answer.)

A: Given integral is as follows

Q: IF A= 3i-2j find A.A *

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Q: Compute / z(r +2) dr. + 2x) +C +z² +C +C O z°(z² + 2z) +C O z° +z? +C

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Q: S(cost x- sin x)dx

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Q: 1. Prove L = re L 0 r

A: Circumference of a circle with radius r is

Q: Eliminate B and a from the relation. x = B cos(mt + a) *+ 2wx = 0 O * + w?x = 0

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Q: Suppose that P(Xi = 1) =pi = 1-P(Xi = 0), i=1,2 If p1>=p2 , show that X1 >= X2.

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Q: [1 ㅇ 1 Let A = 0 -1 %3D Lo ㅇ -1] a. Compute A² and A3. b. What is A1019

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Q: 43x2-2x dx . | Evaluate x + 2

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Q: Q. 5 Given that A and B are independent with P(AUB) = 0.8 and P(B)= 0.3, find P(A).

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Q: Evaluate , 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.  dydzdx dzdxdy…

A: Let us consider the triple integral I=∫E∫∫f(x,y,z)dV then the integral is of the form…

Q: 15. Find x so that m || n. (5x – 20)°

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Q: Evaluate . 2y2 cos(x) dx + 4ysin(x)dy where C is the line from (0,0) to G,0) and then a line from (,…

A: Line integral over the curve.

Q: Show that if an = 3n3-17n2 + 2n-6, then an = Θ(n3).

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Q: (2) For each nEN, set D= [ Find each of the following (2) U Dn. (b)

A: Given Dn = -7n, 5n

Q: 18-19. Find the value of x so that ACAB - AFED. E B x - 1 4, 16 A 8 D 3(x + 1) F

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Q: Show that if an = 5n3 - 14n2 + 7n - 3, then an = Θ(n3).

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Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: Show

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Q: (6) L {(1+ te-t)a}.

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Q: a sin(ry) dA, where R [0, 2] x (0, ] R

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Q: Q2l find the Least-squargs fre Line y=f) - AX+B for the followingdato 2. Ук

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Q: Find the area S of the shaded region in the figure if ƒ (0) = 0² + 30. Note that 0 varies from 0 to…

A: To find the are S of the shaded region in the figure if fθ=θ2+3θ Note that θ varies from 0 to…

Q: Let a = i +43 + 2k. Find ||a||. −

A: Given, a→=-i→+4j→+2k→

Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: If m is a positive integer and x > 1, then show that 1-4¹ (-1)" xm+1 m! 2 F₁ m+1 m+2 2 2 dxm

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Q: dx V1– r2

A: ∫01x1-x2 dx Put, 1-x2=t⇒0-2x=dtdx⇒-2x dx=dt⇒x dx=-dt2 Therefore, ∫x1-x2 dx=∫-dt2t=-12∫dtt12=-12∫t-12…

Q: In x dx = x* +1 now that 16

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