Assume that =y+In(x), and n=x, then u xX а. O a. 1 Ob. 1 1 с. O c. x² d. 1 Unn x 1 O e. x² е. 2 +Unn Of.

Q: If z = e'x + y In(x), find z, and z, Zx Zy II

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Q: Find the most general antiderivative. O se3x + 9eX + c 3 e 3x + 9eX +C Z3x - 9e* + C 7 e 1 3x ex. +

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Q: dz If z = x² y', x = 3, y = t then =? dt Select one: O 613 + 312 O 1 O 2712 O None of them

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Q: Suppose E(X) = 1, V(X) = 2, E(Y)= 3, V(Y) = 4, and E(XY)= 5. (1) Сov (X, Y) (2) Corr(X,Y) (3)…

A: 1) COV(X,Y) =E(XY)-E(X)E(Y)                    = 5-1×3                    = 2

Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

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Q: Evaluate SSS 7e(=²+y²+z?)*² dV over B where B = {(x, Y, z) : x² + y² + z² < 1}. Take T = 3. Turkcen.…

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Q: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

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Q: If f(z, y) – e . In(9y) , then fz is given by: O - 9e In(9y) o - 27 e In(9y) O 9 e In(9y) O 27 e…

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Q: Let z z'y- zy?, z = e ",y = e", then which of the following is ? 3012 O a. 2e- 2e 24 O b.0 Oc-2e-2e…

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

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Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: 2. Given: XW XY, HA I WY, KB 1 WY Prove: AHWA ~ AKYB. K Y.

A: Given data is : XW¯≅XY¯ Therefore ,  ∠XWY≅∠XYW∠XWY≅∠HWA∠XYW≅∠KYBTherefore,∠HWA≅∠KYB     .....1…

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: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 6. If the substitution u = Vx + 1 is made, the integral x+1 dx u? du и? — 1 u? А. В. J, 2(u² – 1) du…

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Q: 1. Prove each of the following results: (a) |zw|=|w-z, Vw, z EC (b) ||zw|≤|zw, w z (c) |z| ≤ Re(z) ≤…

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

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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: H.W: if w=√x2 + y2 + z2, x= erCose, yerSine, z=ee prove that aw/ar = e²r/w and aw/00 = e²0/w

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Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: E=D{(r,0,2): 0s es n, Os zs 1, Vzs rs 1.

A: Given,          E=r, θ, z : 0≤θ≤π, 0≤z≤1, z≤r≤1 To find:           ∫∫∫Ey2ex2+y23dV

Q: Given DE Cauchy-Euler xy +2y In x, x>0 what is the particular solution?? II. -In x+x I x II. IV.…

A: Given that : x2y' + 2y = ln x

Q: EXAMPLE 4: WY = In AWXY: WX = 9 m, XY = 15 m, and n ZW =31° m2X = mZY =

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Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: b) = f ) then prove that x ux + y uy + z uz = 0 u

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Q: m+n If x"y" = (x+y)*** m, n d'y prove that = 0 .2 dx?

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Q: 1. If x, y, z E R, prove that (c) ||x| – |y|| < |x –yl. (d) \xy| < }(x² + y²)

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Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: Express In x V in terms of in x, In y, and In z. 2mx-글 my-글 nz 2 Inx + 글 Iny-글 mz znx+my+nz In y 2nx…

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Q: If u=l0g Cx +ytz- 3>yz) prove that Ce+y+z) he

A: Given that u=logx3+y3+z3-3xyz Then  ∂u∂x=3x2-3yzx3+y3+z3-3xyz ∂u∂y=3y2-3xzx3+y3+z3-3xyz…

Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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

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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: (4) Evaluate : S[(xy? + yz') dV if Q = {(x, y,z): x:[-1, 1], y:[3, 4], z:[0, 21}

A: Note: As per our company guidelines we are supposed to answer only one question at a time. Kindly…

Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: ở =, then If f(x, y, z) = In(2 + x² – 2y² – 3z), Duf(2, –1, 1) = A) % 11 V3 В) 11 C) D) - E) OC O D…

A: The solution is given as

Q: In Exercises 53-58, compute the derivatives indicated.

A: Here given as fx, y=3x2y-6xy4 Now ∂f∂x=∂∂x3x2y-6xy4=6xy-6y4∂2f∂x2=∂∂x6xy-6y4⇒∂2f∂x2=6y

Q: 20 Given that the (bx) +(ay) =(ab), where a and b are constants. Show that-

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Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).

A: X~Gammar,λ fx=λrΓre-λxxr-1,     x&gt;0, r&gt;0, λ&gt;0 Y~Gammas,λ fy=λsΓse-λyys-1,     y&gt;0,…

Q: Show that |Re(z)|+|Im(z)| < v2|z| for any z e C.

A: The solution is given as

Q: al solution of - uy = 0 is O is *+c,e¯*)(c

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Q: he joint pmf of X and Y is given below. What is E()XI-M)? Y -1 1 X 1/16 1/16 1/16 1/8 1/16 1/8 1/8…

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Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

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Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: (a) z, and z4 where z = sin(2x) + y, x = s² – t², and y = s² + t² (b) z, and z4 where z = e*+y, x =…

A: We need to find the partial derivatives z.

Q: 2. Give the condition which ensure that |ez| < 1 where z in C.

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Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.