In domain ech has Surely

Q: 4 prove that 170 is Riomonn

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Q: Cualuate indfin te ntaen Jett dt

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Q: what happened to the 1(1-lambda) part in the first line

A: Given

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

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Q: How many 5-tuples (x, y, z, u, v) of natural numbers satisfy x + y+ z+u + v = 20? Let x= X-1,…

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Q: n) the Integral evalu ate car 1- (X² +3) e Xdx

A: Given integral Apply integration by parts formula to integrate

Q: Find the set of ordered pairs (T0, Yo) for which Picard's Theorem guarantees that the IVP y ry %3D y…

A: Given,            y'=xyx+y, y(x0)=y0

Q: 5.-find the exponential Ronction fa)= ab? tha satisfies the condition f(0) = -4 and f(-3) = - 500

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Q: B = { t,f,-3 is compact. IS %3D

A: See the attachment

Q: Is there anyway to show this is true via Pigeonhole Principle?

A: The pigeonhole principle states that when there are more pigeons when compared to holes, then at…

Q: 4) State the Rank-Nullity Theorem.

A: To state: Rank - Nullity theorem.

Q: -1 1 x+1 coth - In X = 2 x-1

A: We have to prove coth-1x=12lnx+1x-1

Q: 3. Is this sentence consistent? “There is someone who loves exactly those people who do not love…

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Q: Prove 1.10De Morgan’s Laws (ii), which states (A ∩ B)^C = A^C ∪ B^C .

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Q: find the'mters ection d Exe sy,z]= [a,0,31++ 4,-2,178 [+sy,z]=[6,-12,--11]+5 [1,2,4]?

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Q: If In x +In(x-3)=In(6x), then X=

A: The equation is given as ln x+ln x-3=ln 6x

Q: Prove that if AERnxm then rank(A) = rank(AT)

A: If A ∈ Rnxm then we have to prove that rank(A) = rank(AT)

Q: : Does fcz) = Continuous af cis

A: We have to solve given problem:

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: [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: Qend Jamain of functon

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Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

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Q: A ∩ B' = (A' ∪ B)' True or False

A: Demorgan theorem:

Q: 2. K42

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

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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: If 1 A = -9 6 1 6. 2 -T and Q(#) = ' Až, then Q(z1, 12, T3) = Enter z1 as x1, 12 as x2, and 13 as…

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Q: ENcule the peccse dehred etional he indicakd alues if x>1 fl-3)3= -15 (1-)5 f (-1) -7 fl0)= 0 fla0)

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Q: Show that 2Vx < e* for all real numbers x.

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Q: = solve (y² + 2y² + ay +18) dx. (5x³y²-x²y + 17x²) dy

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Q: state formally the Heine-Borel Theorem in R^k

A: Let S be a subset of ℝk. Then the Heine-Borel theorem states :

Q: 1- 9/if it of Prove that yś(-)- TT

A: In the question it is asked to prove y'(0)=π for the given function y=2xcos-1(2x)-1-4x2.

Q: Prove S^2 is simply connected.

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Q: J=3 (x₁+2) 2

A: The given data is  X1=3X2=5X3=7X4=2

Q: flx) = x (x-2)+g Eメとス ;if x22 Show that there exists a S such +hat 1x-2166 implies fex)-8<A

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

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Q: Define 2ndorder linear homogenous/non-homogenousdifferential equationsalong withexamples?

A: To define 2nd order linear homogeneous and non-homogeneous differential equation