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Q: O If fCos,y)=xty-xy%,find Joc-1,y-2. DIf 2=ea>c+ ky oflexx-by), Prove thet baz + ag = 2abz.

A: 1.Given function is fx,y=x3y-xy3. We have to find 1fx+1fy1,2

Q: &2/ suppost se =20, 1} and c={208{ fie ld =20,18 and e= Enumerate the class of all 6- Containing C…

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Q: 9) x² + y² + 12x + 22y + 108 = 0 CX+67² + y +117²=49 CX-47² \ Cy-151²=9 CX-107² + (y +1272²=9 CX-5)…

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Q: O The distibution femetin for eandoy vauiable x m Find (a) The donaity finetim b) He probabitily x)2…

A: Note: As per our Honor code policy, we are authorized to answer only one question at a time. So, we…

Q: Q3. Prove by using logical equivalence method: (pr) V (q+r) = (p Aq) → r

A: Two propositions are referred to as logically equivalent if their truth value is always same. When…

Q: A nB oiaivalar 111222719;10s b) A'U (B n C) 9. Find the number of the subsets and list all subsets…

A: The number of subsets of a set with n elements is 2n.

Q: t FCK and KCK' be algebraic extensions. If both FCK and

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Q: Submit through Canvas as indicated. T u = (2,-5) and v= −3i+7j

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Q: 12 y 2 4xy³z² 4877

A: formula used  xa×xb=xa+blet  A=12x4y8z74xy3z2

Q: tind 16)790) Sorn that ha)=G0g)(x). Letg=2x+3 ha)= 3 12x43 11

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Q: Let Xis Hilber @ 1| + |1

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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: Let F) be a differentiuble func Hen Such that Then g/2)= AS 912)= the equaben of Hhe fagat ine to…

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Q: Derive the eauation of the natu Val cu bic TnterPolat ing sPline for the falowlhg (1,!) , (2,1),…

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Q: let fai) = -x+7| -1-342| whare XER GIue Explietly expression for z y the full Bmupliyind

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Q: O prove that If F is field with IF)= 9=p" then IGh (7)1= (9"-1) (- 4)

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Q: A cosets of of 212 are اخترأحد الخیارات + 2, +1,.1 O + 1,.2 O + 4, + 1, .3 + 4, + 2, + 1 , .4 O

A: Cosets Definition: Let G be a group and let H is a nonempty subset of G. A left coset of H in G is a…

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: Which of the following sets is open in (R, Tu)? OR-(Q-Z) OR-)"2n² :ne N} [2,5) O 12,5) U (1, 7)…

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Q: Prove that ifx, and X₂ are o-fields, then хід Ха is also a o-field

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Q: [2(c056'+isin6")ゴー sin6")ゴー %3D

A: Given:2cos 50+sin 506

Q: 3. prove that: det (AB) = det (A) det (B) a - (; ), » - ( ) 2 -1 7 2 B = 2 в 3 %3D

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Q: Prove that 223 a E lo,1) く 22 + 1영 ( 1-계 3(1-x2)

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Q: Let x, y ∈ R+. Prove that if x ≤ y, then x^2 ≤ y^2 by (a) a direct proof, and (b) a proof by…

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Q: For Jhé fallowing She re LP paoblems, gaph f feasi ble solutions ( f the Ahi Exists) and melhod. One…

A: Since you have asked multiple questions, we have answered the first two questions. If you want the…

Q: 18. fixy=lnx, evaluate limpso f12th)-fias

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Q: for ne J, x is a (1-x)(1+x+x²+.. + x^²) = 1=x^²+₁ variable, prove that

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Q: Show that the set A = {n^2/ (n+1): ne N} is unbounded in R.

A: To prove that the set A={n2n+1:n∈N} is unbounded in R,

Q: 3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b)…

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Q: Suppose that a, a', b, b' are positive integers satisfying a) ab' a'b = b) gcd(a, b) = gcd(a', b') =…

A: Given that a,a',b,b'are positive integers such that  ab'=a'bg.c.da,b=g.c.da',b'=1 We have to show…

Q: As PQR in sicle Circl x²+4=25 Such that & & Rone (3,4) 8(-4,3) fmd <Q PR?

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Q: Assume a1,a2,...,an are positive numbers, a1+a2+...+an=1. Prove: Please use non-calculus method)

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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…

Q: 5 М — 11 Find formulas for the entries of M", wheren is a positive integer. M" =

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Q: Q3)B) Let X is pre_Hilbert space. Prove that (α₁x₁ + a²₂x₂, [²₁=1 P₁y₁ ) = α₁ [₁₁ B₁ (x₁₁3₁) + 11₂…

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Q: Find a given that 2k=, (2k + 3) = 1517 a)5 b) n--3 c) n=1 d) not one of the previous answers

A: 2\sum_{k=1}^{n} k + 3\sum_{k=1}^{n} 1 = 1517Tautologies:A tautology is a formula or assertion that…