Given that r'(1/2) mine I'(3/2) and T(-1/2). = T deter-

Q: T(x,y, z) = x² + 2y² + z

A:

Q: If f(x, y) = xe2y + 6xy, then is dydx given by: e2y + 6 등 2e2y + 6 2 O None of these O 2xe2y + 6…

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Q: xarctanydx + dy = 0 2(1+ y²)

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: To convert the nonlinear DE xy²y' = y³ – x³ to become a linear DE we use the substitution y= u"…

A: Given the nonlinear DE  xy2y' = y3-x3

Q: Find the value of ds / du at u = 2 if s = t2 + 5t andt = (u2 + 2u)1/3.

A: We first find ds/dt and dt/du

Q: Find the general dafferential equatron (t) t 36y () - o lol00lution of the general solution y Co) =…

A:

Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

Q: Evaluate dz where ci) .C is 1z+ Yzl =2 Ci) c is 1ztil=1

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Q: ue of the det e 16 is

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Q: Show that if x', y are the deviation of the variables from their means, then x Yi r=1. Σ 2N - Ox Oy…

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Q: We are also given that eRd, where is that in the solution?

A: The previous answer is not correct....See this answer

Q: Let y(x) be the solution for the DE : y = (x + y – 1)2 If y(0) = 1, thenfind y(4)

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Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: If A = 2x î + 3yĵ – z k and x = t² , y = t and z = t + 2; then the value of ſc À · d¯ from t = 0 to…

A: A = ( 2x, 3y, -z ) and C : ( x, y, z ) = ( t2, t , t + 2 ) for t = 0 to t = 1. We have to evaluate…

Q: Calculate fryr if Ar.y,z) = &r-9*y³-z³. OA foe =-322 OB fye =0 OC None of these OD fye = 3r2-3y2-322…

A: We have to find the partial differentiation of the function with respect to X y and z

Q: Sc ot'(3y)dy

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Q: If a particle is moving with v(x)=1.5(x^1/2) and s(9)=33, what is the position of the particle? As a…

A: Let v(x) denote the velocity of the particle and s(x) denote the position of the particle.Obtain the…

Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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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: If (x, y) = (-V3, 1) , then find r and 0.

A:

Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

A:

Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: s for :   (x,y)-->(1.5x,1.5y)

A: The given transformation is x,y→ 1.5x,1.5y

Q: Which of the following is the general solution to (D-3) (D+1) y=0 Oy = (Ao+ At + A2t?) e + Be Oy =…

A: We have to find solutions

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

A:

Q: Find when r = 2 and s = 0, if: as z = xy² – x – y x = y = ers 1+s

A: Here given that z=xy2-x-y, x=r1+s,y=ers So, ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s        =y2-1-r(1+s)2+2xy-1ersr

Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

A:

Q: af af a²f 1. Given f(x, y) = x' + y* find ax ' dy' dxdy and - дудх

A: Please see the answer below

Q: If x2 + y2 = 2st − 10 and 2xy = s2 − t2, find ∂x/∂s, ∂x/∂t, ∂y/∂s, ∂y/∂t at(x, y, s, t) = (4, 2, 5,…

A: If x2+ y2 = 2st − 10 and 2xy = s2 − t2,To  find∂x∂s,∂x∂t,∂y∂s,∂y∂t at (x, y, s, t) = (4, 2, 5, 3).

Q: If y = x2 +1 and u= Vx? + 1, then at x = V3 equal to du 1 -4 -1

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Q: For any 2 RVs X and Y {E(XY)}² < E(X?E(Y²)

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Q: 3ey , find Given z = dz dz au

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Q: Find nalytical salution to Pnti = (r+)+m possible. an Simplity as much as

A: Given equation is: Pn+1=r+1Pn+m⇒Pn+1=rPn+Pn+m⇒Pn+1-rPn-Pn=m

Q: 2 If [ In(ax)dx = 2, then a %3D 1 e4 4 None es 4 4 4

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Q: - Given y= ela's -x²-In'r, what is y'?

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Q: Given f(x, y) = In(3x² + 5y²) then af dx

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Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: 2 2xy) dy, v es (0, 0), (2, 0), (

A:

Q: Find the antiderivative of: dt/(1-7t)^3 where  u = 1-7t

A: To find antiderivative

Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

A:

Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: O, x = 2, y = dy dz is

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Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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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: 2 If [ In(ax)dx = 3, then a = %3D es 4 e4 4 O None e3 4 e6 4

A: Given that: ∫12lnaxdx=3