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

Q: Use the Chain Rule to compute In(u² +uv). au

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Q: Find the Leplace bransform. of Hhe fure tion ESinut octca to biven that

A: Laplace transform of periodic function: The Laplace transform of a periodic function f(t) of period…

Q: Grien V=In (xity?) show that dye

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Q: Compute : exp(i sin(e¬ni)).

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Q: Let x = {1,2, 3, 4} and P= { {},{2,3} , {43} - っ- %3D nd

A: X=1,2,3,4P=1,2,3,4

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

A: Given

Q: Consider the model Yi Bo +31 Xi + ui Where u = B₂Z; is unobserved. You know that 32 = 1 and you…

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Q: 10* tan væ – In () DIFFERENTIATE the given:

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Q: 4. Find the lungth of le chord amd'its distane from the ankr. A 2.

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Q: Verify that He follow egunbin is an ielartiky Fan o -sino 2 tano

A: We will use various trigonometric formulas to answer this

Q: 5)Prove that (1+sinx)(1+sin(-x)) = cos²x (manipulate left side in order to get right side) %3D

A: We have to prove the given identity: 1+sin x1+sin -x=cos2 x We know that sin -x=-sin…

Q: Find the Fourir for fcae) = (1+x) [-x, ] %3D

A: Given function is fx=1+x and −π,π We have to find the Fourier series of fx. The Fourier series of fx…

Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: Find the reductión Bormula Bor d x In (a+bshmx)"

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Q: IF 2 = +i Sin I) UgE DE MOIVRES THEOREM TO fiND ALL CUBE Roors of 2.

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Q: a) Show that: tan z, + tan z, tan(z, + 2) = 1- (tan z) +(tan z)

A: To prove the formula:

Q: 2)Evaluate exdA ,Ris bounded by y = x² ,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: Show that cosh iθ = cos θ,

A: We know that  coshx=ex+e-x2 and by Euler's theorem, eix=cosx+isinxe-ix=cos-x+isin-x=cosx-isinx We…

Q: Prove %3D 11

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Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: : Does fcz) = Continuous af cis

A: We have to solve given problem:

Q: If Y=tanx prove that %3D2

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Q: prove that. sinh ciz) = i sinz sinciz) zisinh z , cescia)= coshz

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Find y,(x) if y = In(In(Inx)).

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Q: How: e way, prove that By the sam e 王Sinw.k sin Wok

A: Through Z-transformation, we can transform a real time sequence to a complex sequence. The…

Q: Conotrut a onatn'x whode Columu 8pure (leli2) & whole cli5) 10 is spanned by now &pale in Bpanned by

A: Column space is spanned by 3-dimensional vector. Row space is spanned by 2-dimensional vector.…

Q: B) Show that coth-x = In ()

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Q: 2.Prove that I (sinwt) : s2+w?

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Q: Let y = sin(sin(50)). Then y" is equal to: %3D Q7 -25 cos (50) sin(cos(50)) – 25 sin(50)…

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Q: Prove that $lax) =se³ is Cont. on ts don

A: Given: fx = x3 and δ≤1 To prove: f is continuous on its domain.

Q: Use the dddition Rormulas to derive the identitie sinlx-I)= -Cosx

A: Given:sinx-π2=-cosxFormulasina-b=sina cosb - cosa sinb

Q: cos Ꮎ 1 + tan 0 sin Ꮎ 1 + cote = cos 0 sin 0 Suppo pat bus to as to

A: Left side is given by :cosθ1+tanθ-sinθ1+cotθ

Q: How many different rays can be formed from six collinear points?

A: Let A,B,C,D,E,F be the six collinear points.  with first point A and last point F. With the end…

Q: Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0)…

A: We have to find clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the…

Q: Prove that osIl" + sini = tan s 56° cas 11-sinll %3D

A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: Find first and second fundamenta! Texm U-V e Cos 2sin U-V of

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Q: let u = sin" ax = due

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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: Find the upper bound of zdz, where Cis the line segment from 1-/ to 1+ Attach File Browse Local…

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Q: 3 has infinitely many soluti

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Q: I, Let dlP) S-a). End fIt) Sta

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Q: 9 Find the lies which degion bounded and area in in first eyuadrant 12-axis by Jine V= n=770 Give…

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Q: 3,4 show that the integsal (Xy°ty%dx + 3) Independent of the path joining the peints (1,2)and 3,4).…

A: A function F is path independent if it is conservative. And if a function F is conservative then…

Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

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Q: sec 1.)S Intanßtanß dß

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Q: s convex.

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Q: Here is an informal proof that tan¬11 + tan¬|2 + tan¬13 = 7. Explain what is going on. %3D

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Q: Explain the fundamental theorem of albenra?

A: To explain: Fundamental theorem of Algebra