Prove that Srxdr = 2[, , da, r × dr =

Q: prove thats. u.w V.W V.

A:

Q: Prove that Cov (x, y) = E (xy) – E (x) E (y).

A: Cov(x,y) is covariance of x and y. E(x) is expected value of x E(y) is expected value of y.

Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

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

A:

Q: Let r = xi + yj + zk and let r = ||r||. Prove that

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Let u, EC prove that ū · v = v · ū น

A:

Q: Prove: Given that ll Xllo sl1x|1, <vñ lIXloo for XEL". 2 Show that for

A: The matrix p- norm = operator norm                            ||A||p = Maxx≠0 || Ax||p||x||p…

Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

A:

Q: Prove that R is symmetric

A:

Q: Complete the proof that AUVX ATWX. U V T. W

A: Given:  WX=VX and UX=TX. In △UVX and △TWX WX=VX                  (Given) UX=TX…

Q: Show that J74) LOSK +Sinn 2. %3D TIX

A:

Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.

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Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

A:

Q: Let r(t) = ⟨t, t, t⟩. Compute r'(t) and interpret the result.

A: rt=t, t, t

Q: Use the given information to prove that ARST AVUT. V R Given: ST UT ZSRT LUVT T U S. Prove: ARST…

A: ST=UT and ∠SRT=∠UVT in the adjoining figure

Q: Prove that ifx > 3 and y> 4, then xy > 11.

A:

Q: Prove that ||A||1 = max1<j<n{£", |aij|}. %3D

A:

Q: Let x e R,-1. Prove that VNEN (1+x)" >1+ nx

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Q: Find the of im < Re z< £ un der w-

A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…

Q: Let r, y EN such that y # 0, then y+r#0.

A:

Q: Prove that (aA + bB)t = aAt + bB t  for any A, B belongs to Mm× n(F) and any a, b belongs to F.

A:

Q: Prove that da(x) = a(b) a(a), %3D |

A: This is a problem from Reimann Stieltzes Integral

Q: Prove that dl = (Vu) x (Vv) - do.

A:

Q: Prove that f, uv v • dỉ = – §̟ vũu • dĩ

A: Whenever the force is conservative in nature the work done over the closed loop is always zero. i.e…

Q: Let f(x, y, z) = x³ – yz?. Find af af of and ax' dy az

A: Given : fx,y,z = x3-yz2

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

A:

Q: prove that T= S.

A:

Q: use the inner product = p(x)q(x)dx. to find the projection of p(x) q(x) = 5x + 2. = S'; x3 onto

A:

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: Prove that dv du 2 – u? + v² 18

A:

Q: Show that fi(r) = rª and f2(r) = r² +1 are orthogonal on the interval [–1, 1).

A:

Q: Express −i+j in the form [a,b]

A: Simplification

Q: prove that tr(aA+bB)=atr(A)+btr(B)for any A,B belongs to Mmxn(F)

A: Let A=aij and traceA=trA=∑i=1maii.. Note that, aA+bB=aaij+bbij. Then,…

Q: Show that the functions x and x2 are orthogonal in P5 with inner product defined by (5), where xi =…

A:

Q: Find the source Q cx) Such that the So lutiim Uckit) of + Q(x) 2 ə x² 0 < x <∞ | U(x,o) = 0

A: given equation ∂u∂t=k∂2u∂x2+Qx ,       -∞&lt;x&lt;∞            ...iux,0=0 claim- find the source Qx…

Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Let 1 an(r) : u(reie)e ino de %3D Prove that:

A: .

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

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

Q: Prove that −(−v) =v

A: To prove: --v=v

Q: Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

A: Given that, f1(x)= x, f2(x) =cos2x and interval is [0, 90o] Wehave to find that the functions are…

Q: Show that f : R → R is bijective, where: f(x) %3D필

A: A function is injective if f(x)=f(y)⇒x=y. A function is onto if for every y in Y there exists a x in…

Q: (a) Prove that if f e C (R²) then a (af af %3D

A: This is a problem of the calculus of several variables, higher dimensional calculus.

Q: Compute the value of f.dr If F= -yi+xj and c is a from (-1,1Y to CI,1) %3D SemICirele

A: Proceed as shown below

Q: Prove that B (xX+1; y ) + B (x,y+1)=B (X,Y) let П (х+1) = ХГ (Х)

A: We have the formula for beta function interms of gamma function is that B(m,n)=Γ(m)Γ(n)Γ(m+n)As we…

Q: Prove that S[x] = {a+bx where a,b in R} is subring ℝ[x].

A:

Q: J Prove (An B)' = A' U B'.

A:

Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy

A:

Q: Prove using soundness (Required): (∀x)A → (∀x)B ⊬ (∀x)(A → B).

A: The proof is shown below.

Q: Construct AB congruent to XY

A: Given query is to construct congruent segments.