|U( Z Ð Z O Z O Z)[ _is: O 2 O 4 O 16 O 8 .

Q: 3. For f(x, y, z) where x = u – v, y = v – w, and z = w – u: - Compute - Show that of - af af and af…

A:

Q: Let {u, v} be an orthonormal set in R" and let y = v13 u + 6v. Then, y|| is

A: Here, given that u,v are orthonormal. That is: u·u=1, v·v=1, u·v=v·u=0

Q: 1 Usng the eqressions for the volune and area in n-dunensond 2/2 Space givan by Vncr) 11 " and AnG)…

A:

Q: fraea dipnie Smallad Prove non-Commulative rin o4ader 4.

A:

Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

A:

Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

A:

Q: Show that cl S = SU(Bd S) %3D

A: LetS⊆R, claim: closure(S)=S∪Bd S =S ∪ S' by definition bd(S) ={ x∈ℝ/x∉S° & x∉(ℝ-S)°} let  x∈S∪S'…

Q: det (NT) is sPace Toflogecu! and T=0U{un}such that 7Show that (N, Cl is compact slase

A:

Q: 5. prove thatS" erf (x) dx =o CA

A: ddx(erf(x)) =2 e-x2π   I =∫-aa erf(x) dxI= erf(x) x -∫ ddxerf(x) x dxI = x erf(x) -2π∫ x e-x2 dx-x2…

Q: Let D- Evaluate z dv.

A:

Q: Prove that c(u × v) = cu × v = u × cv.

A:

Q: 18, then Ku = 3 and µ4 Af U2 %3D %3D Select one: O Platy O symmetric O Lepto O Meso

A: Solution-: Given: We find

Q: Prove VZEC, V2|z|>|Re z| +|Im z| + |Im z| Vze C,

A:

Q: Let Z, = 2 cis 30° = 3elli %3D Z = In (1 + i) %3D If Z = Z,Z, + Z, Find Z].

A: From the given information. Write the complex numbers Z1, Z2 and Z3.

Q: 2)Evaluate exdA ,Ris bounded by y = x² ,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: Let D-{tx.y.2) : 2+y?s2s 1, z2 o}. Evaluate z dv.

A:

Q: 6. If y = In(r+ 1) In z then what is dy/dr? %3D

A:

Q: let X=R and R={Caro): a ER 3U {8IR3 C Right way totolyy) c heck Ris

A:

Q: O let X be fe VrV Finel ECX) ael E(x)

A: Note: As per guidelines we can answer only one question at a time. I request you to please repost…

Q: 1) Prove that Ym,n EN such thert m¢ nt = n<m using the princdple of in duction!

A:

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: prove that erf (x) dx =o

A: To prove: ∫−aaerfxdx=0

Q: Let D={(txy.2) : x²ny2sz²s 324, z2 Evaluate z dv.

A:

Q: Let E Os 0s n, 0s zs 1, 8Vzs rS 8. Compute

A:

Q: Assume that u = U (x,y) iu differentiible and x =r ca Ô and y=rsin o eapress 2. entinely in termv 0…

A:

Q: prove: sE121y |Re(z)+| Imcz)l

A:

Q: Express In in terms of In x, In y, and In z. O - In x + 2In y – In z O In x - 2 In y + 2 In z O Inx…

A:

Q: 12 २ (४) = dt | २स Prove !- \) ২-০০) = २(-०० ) 3D \

A: Given that Qx=12π∫x∞e-t22dtTo prove:1. Q-∞=12. Q-x=1-QxSolution:we know that ∫-∞∞e-x2dx=π       ...…

Q: Consider Uu=4uzzy u(x,0) = u(x), u₁(x,0) = u₁(x), on the domain -∞<x<∞, 0≤t<∞o. Suppose that both…

A:

Q: 1. Prove with the usual notations that: (b) A + V =- (a) EV = VE = A (c) A= SEZ

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: 2. Show using only the Cauchy-Schwarz inequality that if u,vE R", then || u- v ISl u || +| v | (1

A: Solution

Q: Determine Z- Trans furm in cludig vegiva of con vergence in n 7o メ(At n<o

A:

Q: O Evaluate: | (In a + xe" + Vry) dy

A: Solution of the problem as follows

Q: Let an 1+1/V2+1/V3+...+1//n , Prove {an} is unbounded. %3D

A: Given that, an=1+12+13+...+1n

Q: Let X, , X>, . X, be a vandam of size I For o hormol distribuien with unrur M and $6. IS 5 Xi = 132…

A: Provided information is ;  sample size(n) = 11 ∑i=1nxi  = 132 ∑i=1n(xi-x¯)2 =99 confidence interval…

Q: Prove that (i) Res (tan z, r/2) = - 1

A: Here,we have to prove that Res(tanz,pi/2)=-1

Q: Let X= Ucy) out of standard er dere d unierm and Y= Uc5) out of

A: From the given information, X=U(4) out of 8 standard ordered uniform and Y=U(5) out of 8 standard…

Q: Assume that a1, a2, ..., an E R (with n > 2) such that a1+a2++an = 1. Prove that af+az++a > 1 (Use…

A: Cauchy-Swartz Lemma : For any real numbers  and  the following inequality holds  ,

Q: 2! ODEV de venten egrimin yözyım alonını bulumz eksni etrafioda döndənuess te duçon

A: A=integration a to b y(t) x'(t) dt

Q: 5. If u = ee Cos(alogr) prove that a'u 1(ôu 1 a'u = 0 + r ôr

A: Derivative.

Q: Show for all x, y in R |x+ys]xl + ]y!

A: consider left hand side  and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y

Q: (a) Suppose ƒ: [a, b] → R is integrable and L(f, P) = U(ƒ, P) for some partition P of [a, b]. What…

A: (a) Given that f:a,b→ℝ is integrable and Lf,P=Uf,P for some partition P of [a, b]. To find: what f…

Q: Prove that fdr %3D dSxVf

A:

Q: Set n n and K intgers 1SKE ni Shorw that 2n42 2 - 2n %3D K-I Kニ)

A: Binomial Theorem: According to the binomial theorem, let x and y are any two numbers. Then it is…

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.

Q: 41 Which rector fields are not conservative %3D 2 2 O F(y) = (32²-4y4y² - 2 x > O y,z): O B,C,and D…

A: a.) F( x, y ) = ( x2 - yx , y2 - xy ) = ( P , Q ). If F is a conservative vector field then Py = Qx…

Q: * lnn is © Divergent O Commegent a Conditional © None ☺ Conergent O d O b a

A:

Q: Evaluate the integral. O sV3+4 + C V3+4 + C V3+4 O 5V3+2 V3+2 + C + C In x

A: