The norm of the set {cosh(i nn x},n E N, –-2

Q: Q:05 that the dual Space Show Co is of

A: The dual of c0  is l1  Let f=( f(1),f(2),f(3),...) ∈c0 and g=(g(1),g(2),g(3),...)∈l1.then  we claim…

Q: Suppose at x = x, Vf(x) = 0. What can you say about x if (a) f(x) is convex? (b) f(x) is concave?…

A: In multivariable calculus ∇f is similar to df/dx of single variable calculus & the ∇²f is…

Q: Show that the function a Y1 (x, y) = [21 2] в с Y2 is an inner product on R? if and only if b2 – ac…

A:

Q: For z € C, define Tz: CC by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…

A: Given that: For z∈C, Define Tz:C→C by Tzu=zu. The objective is to verify the given statement. Now…

Q: ® Find the_functian that satisfies the following conditions for some constant Eceficients c,and c…

A:

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R → R defined by T(x)= Ax , where 1 -1 A = -3 3…

A:

Q: Let o be the hypercube [0, 1]". For any f e C[0, 1] show that (). (x1 + x2 + + Xn dxjdx2 dxn = f ...…

A:

Q: Among all rectangular boxes defined by the inequalities 0 ≤x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ 1, find the one…

A:

Q: Q2: In usual topological space (R.T), answer the following: 4- Is [0,1] is arcwise in R? Why?

A: Given that ℝ, Tu is usual topological space. To show: 0,1 is arcwise in ℝ.

Q: To get a feel for higher order ODES, show that the given functions are solutions and form a basis on…

A:

Q: Find the values of a, b, c, d, e, f, g and h such that ax, S(x) = { 6(x – 2)³ + c(x – 2)² + d(x – 2)…

A: GivenS(x)=ax3,0≤x≤2b(x-2)3+c(x-2)2+d(x-2)+e,2≤x≤3f(x-3)3+g(x-3)+h,3≤x≤4such that S(x) is a natural…

Q: Discuss the cosets of { (x, y) | x, y E R, x = y } in (R × R, +).

A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: Given: ZG = ZI, FH bisects ZGFI Prove: GF = IF H

A: Given that ∠G≅∠I FH bisects ∠GFI To prove that GF≅IF

Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: Suppose AE R, v#0, and (A- A)v#0. Use the fact that A is symmetric show that it is impossible to…

A:

Q: graup Consider a dibedral 2. Du= carb: d=b-(ab)"%=D1> Discuss all passible Commulators 'and verify…

A:

Q: A natural cubic spline S on [0,2] is defined by |So(x) = 1 + 2x – x³, S(x) = if 0<x< 1, |Si(x) = 2 +…

A: Given Sx=S0x=1+2x-x3if 0≤x&lt;1S1x=2+bx-1+cx-12+dx-13if 1≤x≤2

Q: Give an example of (v1, v2, v3) and (w1,w2, w3) independent se- quences in the Rº such that…

A:

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: Given: ZG ZI , FH bisects GFI Prove: GF = IF F H

A: Consider that in the figure: ∠G≅∠I and FH¯ bisects ∠GFI. To Prove- GF¯≅IF¯.   Since FH¯ bisects…

Q: Complete the two-column proof. Given: ZB = ZR, ZBPC = ZRCP Prove: ABPC =ARCP R Statements Reasons I

A: Answer and explanation is given below...

Q: Consider f, g E T° (R") and 0 > 0. Show the following results on the subdifferential. (a) a(0f)(x) =…

A:

Q: For z ∈C, define Tz: C →C by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…

A: Firstly, find out Tz*.

Q: 1. In R2, what is the dual cone V* if the primal cone V is V %3D {y1 (-3, -4) + у2 (1, -3) |у »3 0}

A: Given: V={y1(-3,4)+y2(1,-3)|y&gt;=0}

Q: Find a norm of the function flt)= t+2t in space C^co13 %3D where normis given by formula ms x…

A:

Q: The formula in cell C2 is = A$2. Auto fill is used by dragging C2's auto fill box across to D2, E2,…

A:

Q: Express the following tunctrons in the form u+iv f(2)=In (I+z)

A: Solve the given problem.

Q: 1. In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) | y >= 0}

A: In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) I y &gt;= 0}

Q: a. Show that T: 1² → 1² defined by Tx = y = (n), n, = r, is compact where x = (5,) and where0 <r< 1.

A: Show that T: l2→l2 defined by Tx=y=ηj, ηj=rjξj is compact where x=ξj and 0&lt;r&lt;1. Definition:…

Q: The space is CJ0,2r] and the inner product is (f.g) = J r9gt) dt. Show that sin mt and sin nt are…

A: Given m≠n∫02πsinmtsinntdt=12∫02πcosm-nt-cosm+ntdt=12sin(m-n)tm-n-sin(m+n)tm+n02π=0

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R →R defined by T(x)= Ax, where 1 -1 27 -3 3 -6

A: The objective is to find ker(T) and range (T) and their dimension.

Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

Q: An Instructor teaching three sections of vering the same material. She has made ction, but she…

A: By using ANOVA test for a single factor, a) Null and alternative hypothesis: Ho:  µ1 = µ2 = µ3  (All…

Q: Let C:z=1 in the counterclockwise direction and I = . dz, ] = f. Lnzdz, and z+5 K = $, tanzdz. For…

A: Here we will check whether the function is analytic on given region, And then will decide the…

Q: If the Wronskian of f and g is t cos t - sin t, and if u = f+ 2g, v = f - g, find the Wronskian of u…

A:

Q: The Canonical form of a hyperbolic PDE is F (ξ, η , u, ug , un ) %3D False True

A: To check the given statement is true or false. Given that the canonical form of a hyperbolic PDE is…

Q: O let T:R?→R² be a lineas tanafor- mation Such that T([:])- [ ]. T %3D Find matnie A Such that T(x)=…

A: Given that T:ℝ2→ℝ2 such thatT11=41  and T01=32 We have to find the matrix A such that Tx=Ax   ,…

Q: Find a norm of the function f(t) = 2t4 – tin space C0, 1], where norm is given by formula max|f(t)|…

A:

Q: Find the of the GS that satisfies the given Cond hb Sum a n=4 b. h=6

A: Sum of Geometric series.

Q: Complex Analysis

A: For given function, First we will show the function is harmonic function as shown below :From the…

Q: (4) In the figure, Y is compact, BEX*Y. Show that T,(B)s TB) clesed X (T, is the nýuchikn funebran)…

A: Given that Y is compact and B⊂closedX×Y. The objective is to show that, π1B⊂closedX Let's define,…

Q: The norm of the set {e-8inx},n e N, "<xs in the Hermitian sense is А. В. С. D. 8. E. None マド」。

A: Use the formula of the norm to determine its value. The function and the limits are given.…

Q: Show that the dyfferential equatian IS exact x(スt5in t) do + cast -2tu) abe +x² dt-

A: We will show that the given differential equation is exact.

Q: 11 12 10 7. 8 = 1 в «СВD BD = 1 ВС A C E ACDB

A:

Q: which of the sets is orthvoonal under the given inner product on C[0, T] ? = S fusgıx) dx I. {1,…

A:

Q: r = √3 − 2cos θ.

A:

Q: Solve the problem for w(r, θ) in a unit disk ∆w = 0, in 0 < r < 1, w(1, θ) = x2 + y, on r = 1.…

A: Consider the provided question,

Q: P.15.25 If A E M, is symmetric, prove that AT is symmetric.

A:

Q: (f) Find the length of the projection of i onto ū.

A: Given

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.