QNo 1 :- Suppose that fn f (un (umipormly) Set A s R. on (Peintwise ) A S R. cm

Q: Let f: R R be defined as f(x) D 1 + x2 Let /= [- 1, 2), then f(1) = Select one: а. 1] b. (0, d. None…

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Q: Conader the functon 22ty Sz,) = Among the folowng statements, select the ones that are true. Each…

A: using the basic definition of the limit of f(x,y).

Q: Let X is p.d.f and 0 < x < 1, f(x) = Vx, E(x) + E(2x) %3D =......... A) 2 B) C) 3 D) e

A: Given that; X has a pdf.  f(x) = sqrt(x) : 0&lt; x &lt;1 By using expectations property we get…

Q: Corollary 1.1.2 If PA and Pg are two arbitrary partitions of [a,b] then L(f, PR) <U(f,PA).

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Q: Consider the function f : N→ P(N) given by S(x) = {d € N : d|æ}. a) Write out all of the elements of…

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Q: let M be the lebseque measure on B IR) Calcutate (1) Mes), where S = Where S= { Yn t h+3 i) M( n…

A: We know that measure of countable set is '0'

Q: If f is Caib], ab solute maxinum continouus on then f attains valye fcc) and an ab solute mirinum an…

A: Que: Ans : Given         f(x) is any continews function on [a, b]          Let f(c)  be absolute…

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Suppose n E N and u, v € V₁ such that |u| = 5, |v|= 4 and u⚫v=-7 Find |3u + v. Find t R such that u…

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Q: 8.k Let F C RP. try the following items a) F is closed in RP if and only if F = F

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Q: Let f(r) = 4e and g(x) = In(5z): find (f o g)(2). %3D a) O 60 b) O 100 c) O 16 d) O 40 e) O 400 f)O…

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Q: Let fex) and g(x) be two (Piece - wi'se) comtinuous functions on Intervál caib]. Then if t) ¿gCx)…

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Q: * H.W Let f:AC, 9:B D be two functiens sit flx) = 96) ha fug: AUB CUp VXEANB then defred by:. %3D…

A: SOLUTION- SolutionA Rlation R:X→Y, where X and Y are setsis called functions if each element of x…

Q: ス) For each Funci injective, surjectie, both, ar neither. Give short justi ficatiums for you la) A=…

A: 1) f(x) = x2 for injective take two elements x1 and x2   from set A  f(x1) =f(x2)⇒x21=x22⇒x1=x2  and…

Q: 5.PT. PLN has $140000 to invest. The alternative investments and the corresponding annual returns…

A: According tot he given information it is required to form an linear programming problem for the…

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: れお! /0 fi23)=4 4 (か) 2,十 F) Eanals it Ofiles)= 12 D Not if tha above

A: Given: Fx,y = x3y2 To find: Fx2,3 We know that Fxx,y is differentiation of Fx,y with respect to x ,…

Q: sst. Let f(x, y, z) = x³ yª + zª and x = s5, y = st³, and z = s

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Q: Let f(x, y) = x(y - 3) and F = Vf. If r = with 0 ≤ t ≤ 2, then [F. dr is equal to: a. -7 b. -11 c.…

A: We find the line integral in the following way

Q: If 4 p and q P крса are conjugale exponent a measure X a measure space, p р. f₁g:x [₁₂+] measurable…

A: Given P and q are conjugate exponent and f,g are measurable function and let p,q∈(1,∞)

Q: Qt Let T= {carb) a,b ER\fopp and of defined onI by Carb)*(c,d)= (ac, bd) for all (a,b), (c,d ET,…

A: The set T is defined as, T=a, b | a, b∈ℝ\ 0 The operation * is defined on T as follows, a, b*c,…

Q: Let f(x) ={ 2+ Vex-x , for os x 2 } 2 4 evaluate fCx) dx and I f6) dx

A: Given piece wise function as, f(x) = 2+2x-x2    for  0≤x≤24-x                  for  x &gt;2we need…

Q: -5 -4 -3 -2 -1 n y = دیار 2- 7 1 -2- -3- -4 2 3 4 10 5 Write an equation for the function graphed…

A: Given graph

Q: s) Let ICS(P), 4,0, € S(P), and let I (p = 0). (a) Show that then riff I and (b) r, iff r, 0.

A: As per the question, we have to prove two statements related to the consistency of deductive…

Q: O For the function $(x), fla) i defined and lem f Gx) exuts, when is fG) continuous tメO

A: Definition of continuous function: The function f(x) is continuous at x = c when: i) f(c) is…

Q: 12) The value of f, g,f,and g! are given in the table below live f (x) 3. -3 3 6 -2 -1 2. A) Eind h…

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Q: Vove erf C-∞)= -I or J edt=-1 STT

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Q: Find the Maclausin Sesies of The function flz) e Z=7 OT ON itel

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Q: Consider the relation S on N defined by uSy⟺5|(y+u). Is it reflexive?

A: No it is not a reflexive relation

Q: which of the following statements is for t*t, the convolution oft with t" Select one: а. S. T(t –…

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Q: Q4. Let A E Rnxm, n ≥ m. a) Use the SVD of A to deduce the SVD of ATA. b) If m = n and A is…

A: Given: The given expression is, A∈ℝn×m , n≥m a) To use the SVD of A to deduce the SVD of ATA b) To…

Q: ® let the functions: 4:R-A gR-R,with こXe2 Prove that: Tx(4g) =4Vxg +CVf)xg

A: Given two functions: f(x,y,z)=x2eyz3, g(x,y,z)=(x2z2,-xyz,y3ez) To prove  ∇×(fg)=f∇×g+(∇f)×g

Q: If f, g E R[a,b] with f < g on [a,b], prove that g.

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Q: AT If z, y ER" satisty z) + |y|| = |r+ yll, then z 1 V O TRUE O FALSE

A: True and false.

Q: WORX Gavlen flw)=x-d g6)= V-(x-6)" WOP Mekong Delta Find the derivatve Nlx) guven

A: Given:- f(x)=x-2 g(x)=4-(x-6)2+2 h(x)=x-6 We have to find the λ'(x)=? Given that,…

Q: Prove that v5 is irrational.

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Q: and n 12/22 -42 Z+6z Z722+2 2ナ z2, 4z+3

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Q: 5 7. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C X such that…

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Q: (1) Let F =x?++zÂ, and let u= ||FlI. Let fcu) = 3ue 2-2u Show thet Df(u)= 6-6u)eu F -2u

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Q: Prove: If f₁, f₂ € R(a) on [a, b] with f₁ ≤ f₂, then so f₁ da ≤ f f₂ da.

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Q: Assume X = (1,3,5,7}, Y = (1,9,25,49)} and F(x) = x2, such that F:X Y. Then the following is true…

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Q: 3. If f (x) =/7 – x, then which of the following sets is the domain of this function DA) x s 7 |B) x…

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Q: et whose A = T be standard matsix teans bormaton is the lineas 2. 3. Does maps R3 onto R4? s Ta one…

A: Given that T is a linear transformation whose standard matrix is given by A=203032005000. We have to…

Q: Q2 Find fia Inse

A: Solution Given f(x)=(x-1)(ln3x)we need to find the f'(x)