4) Exercie S Hst 2x+iy be a complex mumber such thet (-s(37)#0Then Re (tent3z))|c equal to: Sin Bx co$3 nb (Bx) cosh (3x) $in(3x) cos3x dost(30)+sin Rt (35) Nune bf these.

Q: Q1) Express in matrix notation: x' = (cos 2t) x y' = x – (sin 2t)y +1 z' = 1- x + 3y

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Q: Evaluate (x²sin y-xcos(y)) dy A x²(1+ sin(1))-xcos (1) + C B x²(1-cos(1))-xsin (1) + C C 2sin…

A:

Q: If y = 12y sin(4z) – 12z sin(4y), then (z, y) = 6y? sin(4z) + 3z cos(4y) + h(x) O (z, y) = 6y²…

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Q: Consider the following IVP: у" +у'%3D-сos x;B у(0) %3D а, у(0) -b Find the general solution. A y (x)…

A: Solution of the differential equation

Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: 7. y = tan³ (2³) (A) 3x² sec(2³) tan(x³) (B)-3x2 sec(³) tan(x³) 8. y = cos(5x) (A) sin(5x) (B)-5…

A: Topic = Derivative As per guidelines, At a time only three sub-parts of a question can be answered.

Q: 16. Use Theorem 12 to show that 2n r=0

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Q: Let C be the shortest path that connects a to zi and I = f. (sinhz + 1)dz. Then None of these…

A: Second option is correct answer i. e.  I= -1-cosh(π)+π(i-1) . Thankyou !

Q: Place these trig equations into general form: 1. y = sin (4x + 3π/2) + 2 2. y = cos (3x - 6/7) 3.…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 21.2. Find the residue of f(2) = 1/ Cos z at all its poles.

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Q: Let a, b be real numbers and consider the integral (ax² + b) cos(x)dx. Using integration by parts…

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Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

A: Definition used: sinhx=ex-e-x2coshx=ex+e-x2 Consider the given equation as 5ex-4e-x=Asinhx+Bcoshx…

Q: 19. f(8) = 8 - sin²(20) 9 8sin(20)cos(20) a. f'(0) = 9 32sin (20)cos(20) b. f'(8) = 9 32cos(20) c.…

A: fθ=89sin22θ take derivative f'θ=ddθ89sin22θ

Q: The standard form of 3dy-xydx = 3y3e4x/3  by Bernoulli's equation is:

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Q: 2. Show that the Euler-Cauchy Equation Iy" + axy + by = 0, 1+0 can be transformed into the constant…

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Q: 1. how that { cos(Inx), sin(Inx)} is a fundamental solutions set for x²y" + xy' + y = 0 on the…

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Q: esin 2x [In (cos 2a)]? 2esin 2( cos 2x In (cos 2x) + 2 tan 2] 2esin 2a (cos 2x ln (cos 2x) + 2 tan…

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Q: Differentiate y=excos(x2): y'= A. excos(x2)-2xsin(x2) B. -2xexsin(x2) C. ex(cos(x2)-2xsin(x2))…

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Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: 3. = Cos xsin +xax+a 5/2 3/2 1. Ans: Y= 4sin'x* sinx+ To CAx+4)^- Cax+a) 3.

A: To solve: dydx=cos3x sin2x+x2x+1 Solution Given differential equation can be written as: dy=cos3x…

Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

A:

Q: If f(x) = sin(x)e2x, then f"(x) = A) 3sin(x) e2x + 4cos(x) e²*. B) 3sin(x) e2x + 2cos(x) e²x. C)…

A: The given function is: f(x)=sin(x)e2x to find the second derivative f''(x). For that one has to find…

Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint chow that f (x) = x cos x has a…

A: Given, Cosx =x

Q: + 9y = 9 sin 3x (Let y p = Ax sin 3x + Bx cos 3x.) y = C1 sin 3x + C 2 cos 3x - x sin 3x + cos 3x y…

A:

Q: 1. The loop of y² = x * (4 - x) 2. у %3D 6х — х?, y = x² – 2x - 3. у %3D 2х y2 + 4x – 8 = 0 - 4. An…

A: Question 4 : Arch of y = (1/3)sin(x/3) First find out intersection points :  y = 0 (1/3)sin(x/3) = 0…

Q: when y=cos0 is horizontally factored by a factor of 1/4. y=co s1/4 θ y=cos θ + 1/4 y=1/4 cos θ…

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Q: - Find all solutions for 4 cos x+V3 = 2 cos x if 0<x<2n. %3D

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Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

A: 13:      ∫(2x+1) sin4x dx                14:      ∫x cos4x dx

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

Q: 2.1.1 x(3x + 2) = 0 2.1.2 2x +8x = 3 (correct to TWO decima %3D 2.1.3 (1+ xX1– x)2 0

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 8. 4 6° sin°3ycos *3y dy

A:

Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: 7.2 (A) 1. S sin x dx cos x + C because(-cos x +C) = %3D dx 2. S cos x dx = because sin x 3. S tan x…

A: We need to solve the given integral. This can be done as follows:

Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

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

Q: Compute cos² x dæ. cos 2x +C 4 cos 2x +C 4 2 sin 2x +C 4 2 O cos cos x +C 3 +

A: Formulae:

Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

Q: a3z cos(x – 4y) show that a3z 6. For z = дудхду

A:

Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* - 4e* Asinh x+B coshx…

A: Consider the following equation:…

Q: 1 Evaluate | (x²sin y- xcos(y))dy O 2sin y-3cosy + C 6 -3sin y+2cosy +C 6 x2(1- cos(1)) – xsin(1) +…

A:

Q: 2. For the continuous time periodic signal x (t) = 2 + cos(# t) + sin( t) determine the fundamental…

A: Given continuous time periodic signal is x(t)=2+cos2π3t+sin5π4t                            (1) The…

Q: 4 2 cos y + sen²y cos² y - senty 3 cos² y 1

A:

Q: 37. y = (2x + 1)V2x + 1 38. y = 20(3x – 4)'/4(3x – 4)-1/5 3 39. у %3 40. y = (3 + cos³ 3x)-1/3 %3D…

A: Explanation of the solution is given below...

Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: What is y' if y=x³sin (x²)? a. y'=2r°cos (x²) + 3x²sin (x²) b. y'=2r*cos (x²) + 3x³sin (x²) c.…

A: Solve for the derivative

Q: f5cos(1-5x) dr = O - 5sin (1 – 5x) + C O -sin (1 – 5x)+ C 一 sin (1 5x) + C 5 - O sin (1 – 5x) + C…

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Q: n3xcsC3X)ax 3. S sin2xcsc3x+cos²xcsc3x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Compute z -20 where z is the complex number 6(cos 70° + i sin 70°). (i) 6²º(cos 40° + i sin 40°) 1…

A: To compute z-20 where z is the complex number 6cos 70°+i sin 70°.