Let n 1. We have η p(n) = Σµ(d) ²/12. d|n

Q: Using Part(a) of this problem prove that [*r(e) f(x) dx < [*9(x) a g(x) dx

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Q: If A and B are bounded subsets of R, then prove that AUB and AB are bounded.

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Q: sin² 0 = cos ( sin e 1-sin²0 cos 8 tan 0 sec 0 - cos 8 Trigonometric Identity: (

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Q: Prove that for every integer n > 2, P(n+1, 3) = n³ . %3D -n.

A: Given to prove that for every integer n≥2,  Pn+1, 3=n3-n. We shall prove this by the method of…

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A: (a)   Let A=a11a12...a1na21a22...a2n⋮⋮⋱⋮am1am2...amn…

Q: Cos I 12. secx + tan x 1. sin x

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Q: eimil 2.5 THEOREM Suppose f : D R and g : D→ R, xo is an accumulation point of D, and f and g have…

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Q: Suppose that E (X1) =4 What is the Mean square Err What value of p minimizes t

A: Given: E (X1)=4, V (X1) = 6E (X2)=4, V (X1) = 8 (a) Mean square error of μ^=X13+X22: Expected value…

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Q: An indicator function of the set A is the function on N given by j1 if w e A 1,(w) = {o_if w € A so…

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Q: If A and B are equivalent, does it follow that the two matrices have the same eigenvalues?

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Q: [Problem 1] Prove the following statements formally. a) Let f(n) b) Let f(n) = = log2 (n) and g(n) =…

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Q: Prove Unjustified Claims Justified Claims O KAOBE4COA O is the center of O01 f KAOBEKCOA AB is…

A: The objective of the question is equivalent of the angle.

Q: Prove that for all n € N, 91(4" + 6n + 8) and n € N, 31(n³-n).

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Q: 1.2. [2, 5]U[3, 7]=[2, 7]. EX LET x€[2,5]U[3,7]

A: To complete the proof, one must find that

Q: 8) Suppose A E Mnxn(F) is diagonalizable. Let A1,· , Ak be the (distinct) eigenvalues of A. a) Prove…

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Q: 29. For any odd integer n, n° n² +3 %3D 4 4

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Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

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Q: C B AK What additional information is needed to prove A BAC AKJL by Side-Angle-Side (SAS) Your…

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Q: csce csce + = 2 sec? 0 Csce — 1 'csсө + 1

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Q: 48. Let f be a function defined on ]0, 1[ by : 0, if x is irrațional f (x) = {1/q, if x=p/q; where p…

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Q: Prove in details 81 न्डै ४ (-1) ren 2+3

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Q: Prove that

A: Given:d2ndx2nsinx=-1n sinxd2ndx2ncosx=-1n cosx

Q: cos A+1 cSc A %3D sin' A 3 1-cos A

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A: Recall sin2x + cos2x = 1 Hence, 1 - sin2x = cos2x LHS = 1 / (1 - sin2x) = 1/cos2x

Q: [an] 2. If A is similar to a diagonal matrix D then A is similar to AT.

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Q: Given: AB = BC and MA = PC, ZAMO = ZCPO Prove: ДАMО - ДСРО В M P А

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Q: Prove the theore

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Q: 14) Suppose that an honest coin is tossed ten times. What is the probability that it will come up…

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Q: If G is a graph, then the sum of its vertex degrees is nonnegative and even.

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Q: Prove inf { t IneN}=0 4n : nE IN Prove sup

A: We have to prove that the  Infimum { 1/n | n in N } = 0.

Q: Every cyclic group is necessarily abelian but the converse is not necessarily true

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Q: Prove the property.

A: To prove,

Q: Please prove it

A: Given information: The investigator is specially interested to estimate the parameter u of a…