4.4 Prove that if A is nowhere dense in discrete space (S, d) then A = 0.

Q: Use the Error Bound to find a valve of N for which Error CSN)<1 x 10-9. is 1.5 3x

A: Error bound for Simpson's rule is defined as follows.  For a function fx, if  f4x≤M, then…

Q: Use Newlon's Me thod with the runclion $r(x)=x^{2}-2$ and inilial value $x_{0}=3: to calculate…

A: Givenf(x)=x2-2            and     x0 =0 newton method  xn+1=xn-f(xn)f'(xn)

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° &amp; x∉(ℝ-S)°} let  x∈S∪S'…

Q: 1. Prove that for all x, y ER, max (x, y) = x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y}=-

A: What is minimum and maximum Value: For a given set of numbers, the minimum value of the set is the…

Q: - Show that the norm tion t= aT+B. Use [a, b] onto [0, 1] (7) = 1, ý(7)= T, V т,

A:

Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

A:

Q: Show that both ℝ and ℝ2 may be covered by countably many open balls.

A:

Q: (10) Suppose that the transtormation given by u=2x-g is used on the н наад) A where D integrat…

A:

Q: Let TNN(u,6²). define a faction Fact):= 2t- a, t>a, and Fact):= K (a-), tsa Find the value of a that…

A: Given:

Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

A:

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: if JERLA.b] and it hex)- J(x). except for finite mumber of Paint in Cab] then that he Rlab] prove.…

A: if g ∈R[a,b] and if h(x) = g(x) except for a finite number of points in [a,b] then prove that h…

Q: Let v: DX be a net in X. Then a point xo X is a cluster point of a net v = {xa} if and only if there…

A:

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

A:

Q: Theorem 4.1. if r, s ER and r <s. Then there is q € Q with r <q <s (i.c. Q is dense in R)

A: n,s∈R and n&lt;s Now, s-n&gt;0. By Archimedean property of R, there exists a natural number n such…

Q: Suppose that T(X) is sufficient for 0 and that ^e(X) is an MLE of 0. Show that ^0 depends on X…

A:

Q: 13 = 523411:KER 3is a sbuet 2x+1 wheher Bis 3 If B Decide t so is asbet of TR aboveand bounded find…

A:

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

A:

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

A:

Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

Q: If ø + SCR is bounded above, then .S has a supremum إختر واحداً: ibs

A: I have proved by contradiction

Q: Prove that Theorem 13.1 (vi) using the simple ftn, nonnegative ftn and general ftn. (vi) If X is…

A: vi) From the given information, X is measurable in N.  There exists a sequence of simple functions,…

Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximum possible…

A:

Q: (2) Show that if dim(V) = k (so in particular, T has k distinct cigenvalues), then there exists v e…

A:

Q: 4. Let xn → 0 and (yn) be bounded. Prove xnYn → 0.

A: Hello, thanks for your question but according to our guidelines I am answering just question number…

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

A:

Q: (X,) is a sequence of independent identically distributed positive RVs, where E(X,) = a and EX,'=b…

A:

Q: 2. What is the largest possible c in (1) if X=R² and x₁=(1,0), x₂ = (0, 1)? If X = R³ and x₁ = (1,…

A: Given: c To find: a) X=R2b) X=R3

Q: Let V and W be finite - dimensionl vecter s pace over

A:

Q: 8. (a) Suppose f : [a, b] → R is integrable and L(ƒ, P) = U(ƒ, P) for some partition P of [a, b].…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: If (x* – y*,x – z°) = 0,z = z(x, y), prove: az y3 az +x³z4 ax - %3D ду 3

A:

Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

A:

Q: and further we require that u(r, z) is bounded as z - +oo. Find an expression for the steady state…

A:

Q: A chow that the wsonskian d es will neves become zex0 to8 all spal

A: Here we use the fact ex&gt; 0 ,for all real x.

Q: prove that Sa/Gn has f discription with M-ly ny-l Degrees tof freedom

A: Suppose that xi and yi are two random samples of size n, drawn from a normal population.  Population…

Q: A) If o0, then : w(8)s (+d) W(8).

A: A) Let fx be a continuous function on a,b then for δ&gt;0 wδ=supfx1-fx2 ∀x1,x2∈a,b s.t x1-x2&lt;δ…

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

A:

Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

A:

Q: 2. Let f and g both be of bounded variation on [a, b]. Prove that this inequality holds. Vrag SV+V

A:

Q: 1 : Determine the manimom and Nalve of the function minimumn x'tyス condition under the *+ 2 7?== 1.

A: To find the absolute maximum and minimum of the function using lagrange multiplier

Q: HW.12 Describe in your own words, what is Limear tram furmatim" How the' concept of meant by n…

A: Linear Transformation:      A linear transformation of matrix is changes the original value to the…

Q: Let SCR and let c e R be a cluster point of S. Prove that for each e >0 the set W := Sn(c-e,c+e) has…

A:

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: Assume C and D are chosen at random from {1,2...,n}. Let pn be the probability that C + D is a…

A: The number of pairs (c,d)  with sum m2 is m2-1 for m2≤n and 2n-m2+1 for n&lt;m2&lt;2n. Hence,…

Q: s defined over ai at one point in tl асcordi

A:

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

A:

Q: 4. Find the number of surjections from {1, 2, ..., m} to {1, 2, .. ., n} such that no element in the…

A: We have to find the number of Surjection from one set to another set.

Q: (11) Evaluate |/| 4rydV where E is the region bounded by z = 2a2 +2y? – 7 and z = 1 as shown below;…

A: