Q1. Prove that KT = = -< T', B' >.

Q: Q3 Prove that In Coth x 1

A:

Q: 3) Prove that ae*+be-x a) b b > 0 ex+e~x

A:

Q: Juneten and be fure at lebel aut least thre f (n) : Su

A: As asked we can find the answer as below

Q: Calculate M, for f(x) = 6 · In(æ³) over [1, 2]. M6 ||

A:

Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

A:

Q: 5. Find the on the interval [0, 4]

A:

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: Give the condition which ensure that Je-| < 1 where z E C.

A:

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: If h(x) — За — — 1, j(x) k(x) = 21x? – 26x – 11 , show - 7x + 11 , and - - - - h(x) · j(x) = k(x).

A:

Q: 7. If [G: H] = 2, prove that gH = Hg (18 from 6.5)

A:

Q: - Let X1, X2, ...,Xn~N(0,0) and T = Fi (T),Var(T)

A:

Q: Prove if equal to MPn (W) dx= 2" (n!)" (2n+)! that m is an integer

A:

Q: Q3: Prove that (9":n e Z) (3":ne Z) but (9":n E Z) (3":n E Z).

A: We have to prove that 9n:n∈ℤ⊆3n:n∈ℤ but 9n:n∈ℤ≠3n:n∈ℤ

Q: Suppose s(t) = 3t+ 6 on the interval [1, 4]. What is the displacement on [1, 4]? 06 08 09 O 18

A: topic-displacement

Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: 4. What is the value of k ?( Let P(t) = 246.7 and P(0)= 226.5 at t =10) А. 0.00243 В. 0.000854 С.…

A: As bartleby expert we are required to solve only one question.  Answer : k= 0.00854 Hence option C…

Q: 4. Explain why (* + ÿ) + (ž + t) equals MQ in the following diagram.

A: answer is in next step

Q: Prove that 12) d SIAX 13)let y=x, find Ay/Ax

A: Derivative of function

Q: Q3: Prove that (9":n e Z} S {3":n Ee Z} but {9":n e Z} (3":n E Z}.

A: To prove:  {9n:n∈ℤ} ⊆{3n:n∈ℤ} but {9n:n∈ℤ} ≠{3n:n∈ℤ}

Q: 2. Find p and q such that |5x - 2| ≤4 implies Ps 23x-4 5 ≤q.

A: Given |5x-2|≤4

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p&gt;1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x&lt;0 when…

Q: Let P = {p:p=6x-1, for some x EZ} and Q= {q:6y+5, for some y EZ). Prove that P= Q

A:

Q: 1 Show that n2 + 1 IN V

A:

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

A:

Q: Prove that Z(Sn) = {e} for n ≥ 3.

A:

Q: Q4 Prove that E(",") = ("::)- () .n 2mzr. %3D +1 +1

A: we have to prove that                                                   ∑k=0mn-kr=n+1r+1-n-mr+1 now,…

Q: Let q E Q and x E R - Q. Prove that q + XER - Q.

A:

Q: Show for R(t) = e?-t and S(x) = 2x + 1, that (Ro S)(x) = e1²+2#.

A:

Q: 1f itwas x25ect, yatunt prove Thut dy

A: Simple derivative

Q: By using Caushy Riucman Prove that? e ae

A: We will use the following result :  Result : Let the function f (z) = u(x, y) + i v(x, y)  be…

Q: 6. so be it r = 3xi + yi – 2zk and f (r) : -- where |r| = r find all of grad(f) and div (-)

A:

Q: 28. (a) Prove that for x e R" and s < t, Ds(x) C D;(x).

A: The notation Dsx represent  an open ball of radius s, centered at x∈ℝn. Let x=x1, x2, …, xn,…

Q: Then k is equal to

A: We know that integration of density function over whole range of x, is always 1. We will use this…

Q: F(p), then prove that

A: simple use of integral transformation

Q: Under normality, prove the followings (a) B~ N(B,0²(X'X)-)

A: It is known that β^=X'X-1X'Y. Here, Y follows a multivariate normal distribution. The regression…

Q: Q3/A/ Prove that ) + ",) = C). %3D إضافة ملف

A: As per our guideline we are allowed to do 1 question at a time. I think you hav already done 2…

Q: (a) Prove the following property: (:) - (.".)

A: Hey, since there are more than two questions posted, we will answer the first question. If you want…

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: Suppose x, n ∈ N and n not equal to  0. Then, show that xn is positive if and only if x is positive

A: Given that x, n∈N and n≠0. According to question, N=0,1,2,3,4,5........ First suppose xn is positive…

Q: 24. Find the Fowrier r fas - -IN X

A: Hv

Q: d. What happens if P < M for all t?

A:

Q: D. Let Find 2,-

A: We will find out the required value.

Q: 10.) For n>Liestablish that the in teger nc an't 5) is of the form ok. or n21, establish the in nz1…

A: To establish given relation we will use first principle of mathematical induction. For this we will…

Q: Use Simpson's Rule with n = 4 to evaluate [² (t³ + t) dt

A:

Q: 5. Let TE B(H). Show that (ker T)- = ran T.

A: Given: T∈BH and T† is an adjoint of an operator T. To show: ker T⊥=ranT†

Q: Q3. Let z, y be real numbers such that ry 1 and z #y. Prove that

A:

Q: 3 (a) Given that T= 2n12g , express I in terms of T, g and n. %3D

A:

Q: Prove the following:  if x^2 = y^2, then x = y or x = -y.

A: Subtract y^2 from both sides.

Q: Ql/prove that : 11=00 H(elw) = Σ 71=-8 h(n)e-jwn

A: "Since you have posted multiple questions, we will solve only the first question for you." To Prove:…