.3 If U = 2 – x, | x/2- xdx= = n} .3 -J uvūdu В (2 – u)/ūdu | .3 © (2- u)/ūdu 1 (D uvūdu A)

Q: (a) Show that y for the given z = e" In x+ xy

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Q: 4. Evaluate fe fds where f(r, y, z) , ) and 0 <t< 1. = 12r2 and the path C is given by r(t)

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Q: 3-If u(x),v(x) and w(x) Find d/dx of (uvw)

A:

Q: 4. Suppose is a discrete rv with E(9X + 2) = 20 and E(X²) = 13. (a) Find E (X) (b) Find V (X)

A: a) We will use the formula E(aX+b)=aE(X)+b E(9X+2)=20E(9X)+E(2)=209E(X)+2=209E(X)=18E(X)=2   Answer:…

Q: 2 al S ex+y dydx

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Q: .'( , "ג oa3 (125x*y)" 学 A: 125 2 3 $%% 1/3 5メ Y C: D: VONE OF THESE

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 2. given that y = 0 at r=1

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Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: - If W = xy + y2+1 azw Show that a2w ey %3D дхду дудх

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Q: Show Sn+3 diverges by osing 6n +5 the test for divegence 1こV

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Q: Find dy/ux of the following 1)lf y = 1/ (1-u) and u = 1/ (1+x)

A: Given y=11-u and u=11+x

Q: 25-x² dx In if we let u = V25 – x , then udu =-xdx.

A:

Q: ppose X1,...,Xn are i.i.d.U(0,θ). You want to test H0: θ=θ0 versus H1:θ < θ0 at level α? Derive the…

A: The given information is: Xi~U0, θ or fx=1θ,   0&lt;x&lt;θ The null and alternative hypotheses are:…

Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

Q: If W = xy ++1 azw Show that дхду ey a2w %3D дудх

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Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: S dy 7 y2-8y+5

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Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: 1. Differentiate the following with respect to x: a. y= 5x - + 5Vx + 3p ex + In(x) - 7 (9)

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Q: dy 3. Find dæ if y = In (aVæ +1).

A: Given,            y=lnx3x+1

Q: Fird XCK) is X(2) = 2くz-)(マ-3) Ans; SC) ャu(k)+と)uck)

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Q: e. y= (x² + 4)/x in the interval 1<x<4. 8+ 4ln4 - % s.u ans.

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Q: If a > 0 and [[ 20*+v 20+u° dr dy = 1(e* – 1) , a =?

A: Using polar coordinate evaluate the above integral

Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: Eva 6 SSin'z osx dy

A: ∫undu=un+1n+1.     cos2x+sin2x = 1

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: 3- prove that w comport dx =w dy yx 23 34 if w=: w = xy² + x³y² + x³y

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Q: of fxyl = 3X-y+6 Subjected QI Find to x+y=4 extrume v alues

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Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: 5) Find NV ir ZN -- 20 7) Find DW if YW-4

A: Consider that the centroid divides the median in the ratio 2:1 (5) ZNNV=2120NV=21NV=202NV=10

Q: If utt 4ura u(x, 0) = e", u4(x, 0) = 0, u, Ux → 0 as x → ∞, then u e* cosh(2t) O e2 cosh(4t) O e2¤…

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Q: An M.V.U. is unique in the sense that if T, 1 M.V.U. estimators for y (0), then T, = T, almost

A: A sample statistics t is said to be unbiased estimator of population parameterγ(θ) if expected value…

Q: Please see the attached problem. Thanks!

A: Given:

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

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Q: 3. Obtain the 6.S. sy dx + taydy = 0 xcos

A: We have given equation  xcos2y dx+tany dy=0 xcos2y dx=-tany dy x dx=-tanycos2y dy x dx=-sec2y tany…

Q: Ques tion 1 : that Given 2 x?y" + x y' + 3y= 0 show 2x* ylara) lanni)x ylurs) + (2n2.n +3) ym)-

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Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

Q: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

A: Please see the answer in Step 2

Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

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Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: If you are trying to solve f et dx and you let u = e then: dv = du = v = vdu Write down the uv –…

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Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: 1. Evaluate | (x- y)ds over the path C:r(t) = 4ti + 3tj for 0 <t<2.

A: Answer

Q: If s = 3/t + 1, then ds Preview %3D dt

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Q: IF Y = u²-1 u²+1 Find dy np

A: Given,  y=u2-1u2+1

Q: Let flt.v) = v+3t°e'. -2 -y + 3t2e'. Then f satisfies a Lipschitz condition in y with L = 2, given…

A:

Q: ds if s = dt t Find 7t +2

A: S=t7t+2 We need to find dSdt