4.Suppose f >,0 and fdu = こ0 Prove that u({wif(w) +o}) we say f=0 almost こ0 tveryuhere (a.c.) with respect to M.

Q: B. Prove each item (Item 3 & 4) of the following by constructing a proof by element arguments 3.…

A:

Q: 4. If [æf (x) + 2] dæ = x³ – a² then find the function f (x). 3 A) 2 3 B) 2+ C) 3- 2 E) 2– D) 3+ --…

A: The given equation is x∫x fx+2dx=x3-x2.

Q: QUESTION 5 3-1 The valun uf s of fox)- in the interval (1,0 such that f- 31-N) OA 3 OB. 3. В. OC 3…

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Q: prove if P>-l then Citp = I+np %3D n€ IN

A: The given statement is not TRUE. Counter example is taking n = 2.

Q: X+Y 4- If X ~Exp(Ø) , Y ~Exp(Ø) then g = О a) Еxp (20) O b) U(0,1) c) Chi-square with 2 degrees O d)…

A: Exponential Distribution: A continuous random variable X is said to follow Exponential distribution…

Q: 5.3.2 (a) Suppose that n > 3. Prove that ("+1)ʻ 5.

A: Given:-             n+1n2 < 2 n+1n2 -22<0n+1n+2n+1n-2<0n+1n+2 =…

Q: Verify the &-ô identity: Ejkɛipq = djpôkq – djqðkp. Then use this identity to show that (a) EilmƐjlm…

A: The given identity is εijk εipq=δjp δkq-δjq δkp  where the εijk is called the alternating tensor or…

Q: 11. Given /(r)-V1-2, fnd onctions /and g so that. /(r) (/o9)(r).

A: Here, we must express H(x) as a composition of two functions. This can be done in multiple ways. One…

Q: B. Prove each item (Item 3 & 4) of the following by constructing a proof by element arguments 3.…

A:

Q: COSZ 2) if Res(f,x) of the function f(2)=- a) -3/8 b) #-6 2ti c) 1/e d) 8/5 -is

A: To find Resf, π of the function fz=cos zz2 z-π3.

Q: Psuppose that fandg are Funcnans. severalvaiverof ECA), F()19g(x). and g'ex) aregiven below. Use…

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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: Given that x>0 and y>0 proof that xy>0. (x,y are integers)

A: Given that x>0 and y>0, then to prove that xy>0. x, y are integers.

Q: if it was Nlo11). Prove that F(2) = 1-F(2)

A: Step 1:We know,  F(z)=2π​1​∫−∞z​e2−t2​dt, so F(−z)=2π​1​∫−∞−z​e2−t2​dt. Step 2: By using the…

Q: 15. Show that if f: A- 1 f(GnH)=f(G) B and G, H are subsets of B, then f-¹(GUH)=f(G) Uf (H) and nf…

A:

Q: Q31 a) Prove that Re(iz) = -Im(Z)

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Q: Which of the following function is NOT Q, (n)? А. п —333п? nlgn С. п-1gn D. 219 n E. None Е.

A:

Q: 6.) Derike the binomial idendity nent) (un-) C Hint: For mzz, c^)+2(^) +m?]

A: To derive the binomial identity22+42+62+.........+2n2=nn+14n-16

Q: n(A u B) = n(A) + n(B) – n(An B) A) True B) False

A: Verify whether nA∪B=nA+nB-nA∩B is true or false as shown below.

Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

A:

Q: Use implicit differentiation to find an equation of the tangent line to the CUNE at the X²y² = (x +…

A: The equation of tangent to the curve y=f(x) at point (x1,y1) is given by(y-y1)=dydxat…

Q: 2F. n 1 ;;1=2" (b), (26)

A:

Q: Show that 2"=nCk and 0 = [(-1)^nck k=0 HINT: Consider(1-1)" and (1+1)" k=0

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Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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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: The value of c of fo-2- in the iterval .D such that rio--E) OA 3 OB. -3 OC 3 O0. 3-

A: c = 3explanation is given in below step

Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

A:

Q: If X~ Uniform(b, 1) and o² = 3μz, what is b? (a) -0.82 (b) 12.18 (c) 20.82 (d) 17.00 (e) None of the…

A: To find the value of b, we first need to find expressions for the mean μX​ and…

Q: Let G = (a, b | a² = b4 = e, ab = b³a). a. Express a'b’abab³ in the form b'a', where 0 < is1 and…

A:

Q: let it be T=11,2,3 } S:la,b,c] Proved P(TNS)E P(S)NP(T)

A:

Q: 17. Use Theorem 4.7 to prove that Vx + 3 2 V3 + x/4 for

A: Let,

Q: 1(42). M = "+ x/F + 78 +1=24 S

A: According to answering guidlines we are doing first question if one or more question given

Q: 5) Given f(x) = V1 -x² , the range is: a) O (-∞; -1] b) O [-1, 1] c) O All real numbers d) O [[0,…

A: The graph is shown below:

Q: Fin Sup(S) and Inf(S), Where 1 S = {1. п

A: Consider the set S=1, 12, 13, ... , 1n, .... Observe that as the value of n approaches to infinity…