. Show that if an = 3n3 - 17n2 + 2n - 6, then an = Θ(n3).

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

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Q: z = If X – y show that: =D0

A: Given: z=xyx-y And x2∂2z∂x2-y2∂2z∂y2=0   As we know that; The Quotient rule; fg'=f'·g-g'·fg2 The…

Q: dy will be dx In x+1 If y = then 2x3 - 3x' (2x- 3x) +1)- (In x+ 1)(6x? – 3) (2x – 3x)? A. (2x - 3x)…

A: To find the dy/dx of the given function

Q: Find the general solution of the following ODE's: y' + 3x²y = x²

A: The given differential equation is y'+3x2y=x2 It is of the form of linear differential equation…

Q: 1.Suppose that (ax+b)cos x dx=6.Then the values of a equals a) c) 4 -4 b) з d) -3

A: The solution of the problem is given in the next step.

Q: 8. If fx) = cos (2x), findf '(). TC %3D a. b. c. 1 d. -1

A: The given function is f(x) = cos2(2x) Differentiate with respect to x using chain rule…

Q: If I, = S e cos" xdx, where n > 2, prove that In 1+n(n-1)In-2 n² +1

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Q: If the rst line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: Given,  The first line  Ax + By + C = 0  and  is to pass through the origin  The second line  Dx +…

Q: If the first line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: The first line is of the form Ax+By+C=0and the second line is of the form Dx+Ey+F=0 As the first…

Q: (a) Show that: (i) dim R" = n (ii) dim R2×2 (iii) dim Pn = n+1 = 4

A: Basis of a vector space: Let us consider a set S⊂V(F) is said to be basis of vector space V over…

Q: The convolution of e2t ® sin(3t) S is | e2Usin(3t – 3u)du e2usin(3t – 3u)du Se-2usin(30)du…

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Q: Find L[e2t tsin(2t) + et+1 + et cos 2t] A)+ 28-4 s+2 (4-1)2 +4)a (+2)a +4 +2 B) 4-4 1-2 1-2 (-1)2…

A: Use the formulas below to calculate the Laplace transform.

Q: 2eln In cos 2t 8 + 2 None of the choices Option 2 2s s2 – 2 s2 – 2 Option 5 Option 3

A: This question is based on Laplace transform.

Q: dx = . If 'a' is

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Q: Q1: Determine -8 sec 7x (-4 cos? 7x + 6 tan 7x) dx. 32 sin 7x – 7 48 sec 7x + C 7 A -- В -224 sin 7x…

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Q: Find the general solution of the ODE. y" +9y = 6 cot²3x

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Q: in Let z = 0.5 +",., Find e 6z 3 C) e3 F) e-0.5 (cos 2 + isin2) A) -e 20 B) e-5* (cos 20 + isin20)…

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Q: If the root of C.E. are (-2, -2, 0, ±2i) then yH = (a) A + Be-2x + Be-2* + Dcos2x + Esin2x (b) A +…

A: We have to find the following

Q: ( 5) Find f (o) and f (0) f Ga)= .3 if x° Cos (x3)

A: Taylor series expansion

Q: .3 If U = 2 – x, | x/2- xdx= = n} .3 -J uvūdu В (2 – u)/ūdu | .3 © (2- u)/ūdu 1 (D uvūdu A)

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Q: 15. sin(2t + 글) dt = e2t-3 8. 7 4 7 64e3 7 4

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Q: What is the general solution of the following ODE* 3 points (x² + xy – y*)dx + (;x² – 2xy) dy = 0

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Q: 21 14x + x4 Evaluate 16 dx - O 7a? + 7 x3 – 16x + C, Where C is the parameter O 7x? – 7 x-3 16x + C,…

A: As we know that: The sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 Given:…

Q: 7) [ysin x'dxdy ans:(cosl-1) 6.

A: We use change of order of integration method to solve the given integral. We change the order  dxdy…

Q: 1. a. Let In = exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or otherwise,…

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Q: (6) Euter eio_ el" = Cos e +i Sino, whore i = J1. where i= JT,

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Q: [ u#(u – 1)"-1 đu (1+x!/n dx = n

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Q: Use the theorem of Leibniz in the following problems: If y=x³e2x find y(m) and hence y(3). julm) =…

A: Leibniz rule states that (f(x)⋅g(x))n=∑r=0n Cr nf(n−r)(x)⋅gr(x) Let fx=e2x and gx=x3

Q: If y=C,cos2x + C ,sin2x + 2sinx is the general solution of a certain nonhomogegeous LDE, which of…

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Q: 2) Show that La- (1 – x²)P',(x)P'm(x) dx : 21(1 + 1) Sim. 21 +1

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Q: What are the conditions on A, B and C for an ODE of the form Ay'' + By' + Cy = 0 to have solutions…

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Q: -1 6 1. Let A= - 3 4 14 4 Fund a) M, and Cl b) Mu3 and C43 c) Fund detA by a Cefactor ex panesion…

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Q: Find the DE of the following by eliminating the arbitary 1. tanx-2x3y=c

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Q: (-1+i/3)°, by using deMoivre 's theorem

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Q: K (To - T) if 0 <TST. if T, ST y (0) =A

A: Given, dydτ+αy=kτ0-τ , 0≤τ≤τ00             ,τ0≤τ  and y0=A

Q: cos 4x = cos 6y, which of the following is correct? 2x + 3y = 90⁰ 2x + 3y = 270⁰ 2x + 3y = 180⁰ 2x…

A: Given query is to find which statment is correct.

Q: 2. -4 let u= dx=

A: Indefinite Integration using substitution

Q: 1. Given A= For which value(s) of a and b will A be singular?

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

Q: a. 2,526sinx + 2,526cosx Yp 29 b. yp 89 3 M 7,930sinx + 7,753cosx 91 3 = c. Yp 3,290sinx +7,753 cosx…

A: We will find the particular integral.

Q: 2 7 4 is S cos' xsin xdx 비

A: See the details solution in below

Q: 1. Given that X1 = 1 X4 =-2 Xs = 4 X6 =-1 X7 = 5 X2 = 3 X3 =0 Xg = 2 X9 = 10 %3D Γind (a) E X;, (b)…

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

Q: 7/2 Q5:-(3t°-2t* – te 3sin 6t +4 cos 4t)eC + t e3t -St As 360 48 (S-2)5 (s-2)5 18 (s-2)²+36 4(S-2)…

A: Answer of question (i) has  typing error

Q: If u = tε-1/2 and inner (t) = A(1 − e−²t/€) and Touter (t) = 2 cos(t) what is the composite solution…

A: As per the question we are given the inner and the outer solutions of a perturbed system as :…

Q: Find u(x, t) which solves the problem Utt = 9urr -00 < x < o0, - 0 <t <3; 1 u(x, 0) = 1+ x2 Ut(x, 0)…

A: D'Alembert Solution;    u(x,t)=ux,t=12f(x+ct)+f(x-ct)+12c∫x-ctx+ctg(ξ)dξ where u(x,0)=f(x),…

Q: 4 Ruret MC w co , , d, 7 the y a Fid e co f de

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Q: If z = x2 – y2 and x = t cos 2r and y = r sin t , then a²z is (A) 2 cos?(2r) + 2r² cos²(t) – 2ry sin…

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Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

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Q: Evaluate L{cos (3+2t) } scos3 + 2sin3 A s2+4 scos3 – 2sin3 B s2+4 (s+3)2+4 (s+3) 2–4

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