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Q: 10 of 17 If y(t)+(t-r)y(r)dr=t, then y(t)= Su-nyndr3Dt,

A: Convolution Theorem: The Laplace Transform of the convolution of f(t) and g(t) is:…

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: Show that a fomws with R>o Ssee igue] may be descuibed panometuicaly by u cU,N] Cosu, (R+ o…

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Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

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Q: Use Newlon's Me thod with the runclion $r(x)=x^{2}-2$ and inilial value $x_{0}=3: to calculate…

A: Givenf(x)=x2-2            and     x0 =0 newton method  xn+1=xn-f(xn)f'(xn)

Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

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Q: Find yas a fon chenof x if t. %3D with

A: This is cauchy euler equation and we will solve it by changing the dependent variable

Q: alue of the pur C: |z| = (:-1)(z-

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Q: Find the fowien senies fon | X), -T<X <A

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Q: 12, Show that ()() = (OC)- n-m' %3D 13. Show thet (A)

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Q: 6. If y = In(r+ 1) In z then what is dy/dr? %3D

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Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

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Q: (o, 1,) 1. find th directional denivatve in the dire chons of at 2 Gve inter pretahon of amp uted…

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Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

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Q: If U(x,y)=In(x²-y²) then Ux+Uyy= XX .....

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Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: in(Zg++s)indeyclic grauf2enerated by I, Z,3

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Q: Fin d the sc cond soluhen prr tk edo te edo If Konow that y, =x IS a solotień

A: We will reduce the order of the given given second order homogeneous differential equation using the…

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: ronskian of the DE : xp(x)y' + 3y = 0 = er² et? et?

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Q: Четверг show that the inu of a bounded E tix-oy ne 7 8. use T

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Q: If U(x,y)=In(x²-y³) then U+Uyy= ....... ....

A: The solution is given as

Q: prove: sE121y |Re(z)+| Imcz)l

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Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

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Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: (2) If U = (1 – 2xy + y²)-³ prove that, x- = y?U® %3D

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

Q: If utt 4ura u(x, 0) = e", u4(x, 0) = 0, u, Ux → 0 as x → ∞, then u e* cosh(2t) O e2 cosh(4t) O e2¤…

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Q: If (a + bx)e = x, prove that x’y, =(xy,-y)

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

Q: 13- dy + 2xy = y diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? -x* +c1 y = e a)…

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Q: 火2sin C&) for ダチo fcx) = { for x =0 show that Con tinods or not

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Q: 2 la), Pu (aw by Re currence relation

A: We have to find out P2(x) and P4(x) by recurrence relation. We know that the generating function…

Q: true or false without justify The sel { 1,2,t, 3,,4,+, csx, coss is mot Ti Bomded in (CToi], Ul6)…

A: True.

Q: Prove that du Inlul + C where n= -1 u

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Q: -64- Eke n Calcul afe th udlue of Z.Z ?

A: according to company rule we answer only first question and rest can be reposted.

Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm &amp; integration formula of sech(x)

Q: Let X= Ucy) out of standard er dere d unierm and Y= Uc5) out of

A: From the given information, X=U(4) out of 8 standard ordered uniform and Y=U(5) out of 8 standard…

Q: 2! ODEV de venten egrimin yözyım alonını bulumz eksni etrafioda döndənuess te duçon

A: A=integration a to b y(t) x'(t) dt

Q: Show that for all x, y E F, there exists e with e < Emachine such that fl(x * y) = (x * y)(1+ €) is…

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Q: See image below.

A: Given that the tangent line touches the curve y = f(x) at (4, 3) passes through the point (0, 2).…

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

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Q: Prove that S, pm (x)Pn(x)dx = 0 if m# n ? %3D

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Q: 10- Prove that a.b3D la+bl2- la-bl? /4

A: Prove that a.b= la+bl²- la-bl²/4

Q: Suppose that the true model is () E+ and that it satishes MR1-MR6, but you estimate by OLS (II) W=…

A: From the given information, I yi=γxi+ei The OLS estimator of γ is, γ^=∑i=1Nxiyi∑i=1Nxi2 II…

Q: 4: a) Let X.X., X -N (Hi,6f). Let Y,, Y2 Ym-N (u2,63). .... d (1-a) % CIfor oi when ai. a known.

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Q: Show that lm Casy -1 CoSy-1

A: