a) f(z) = 14/(z2 + 2z + 2) is a complex function, find (1/Tt) S-00° 14/(x²+ 2x + 2)dx

Q: 1 2 de 4-cose %3D II

A: Given,          ∫0π214-cosθdθ

Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: Approximate (a) cos 0.8 and (b) cos 1/2 using the linear approximation technique

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Q: (7) Find the lengths of the curve r =2/(1 - cos 0), a/2<0<n.

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Q: F(x) = 1+e siny x %3D -- = -15 e sin4X- se"co54X fca) = fco) = -8 R fくり) = fci-2) = 4.2398 > KMS %3D…

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Q: ст/2 56. " sin(2 mt/T – a) dt -

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Q: 3. [(3t +r*)sin (21)dt /

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Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

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Q: use two and three points of Gaussian-Quadrature method to Find 1 = e" e(1+sinx) dx

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Q: 6. (a) cos 2x dx; u = 2x

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Q: a. Prove that the O.D.E: (2y+2x-5)dx+(6y+2x-1)dy=0 is exact and solve it.

A: First we will check if this equation is exact.

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

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Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: 3.4.4 Evaluate ff sin(x + y) dx dy over the triangle whose vertices are (0, 0), (2, 1), (1, 2).

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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: (a) /4 1+3 cos² 1 d.x; COST dx3B

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Q: 3. Solve the DE dy = x + 2x %3D a. dx 3 dy b. dx %3D dy C. -= 4 cos 6x %3D dx

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Q: Find the solution. (Dª+2D3 + 10D2)y =0. @y = c,e-+czxe¯+e"(e,cos3r +c,sin3x) y = (c,+c,)x+e*(c,cos3x…

A: To solve the given Differential equation.

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

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Q: Solve the he o-3D+4)y(x) =x cos(2x) equation y,(x)=(6x+4)sin( *+4)sin(2)-cos(23) - y,(x) =(-6x-4)…

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: (b) у" - 4у %3D (2? — 3) sin(5a

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Q: . у" — 8y' + 16у %3D е 2x sin 4x + 2e4x + 5х

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Q: Find all values of the complex function of z for the e^(3z)=1z=x+iy

A: Its given that e3z = 1.  Given, z=x+iyWe need to sovle for z.

Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

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Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: (a) Use the method of undetermined coefficient to find the general solution to the inhomogeneous…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Example 1: Find length of the cardioid r = a(1 – cos 0) %3D | from 0 = 0,0 = 2n

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Q: che general solution of -V - 6y = 6x3 + 26 sin 2x

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Q: Find one particular solution to the following second-order forced equation d²y + 2y = cos (√2t) dt²…

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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: b) y" + y' = sin 2x

A: here we need to find the particular solution of given differential equation. the solution is…

Q: The annihilator operator form for the function e + cos(2x) is:

A: The annihilator operator form for the function ex+cos(2x) .

Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: 4 cos 2y-3 dy 2у

A: NOTE: Refresh your page if you can't see any equations. .

Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

A: From the given differential equation; D2-3D+2y=14sin2x-18cos2x So, the auxiliary equation is:…

Q: 2. 3. ત્ર 6 -1 cos²2x dx X - dx

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Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: Find the general solution of: y"-3y 8e* + sin 2-

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Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

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Q: 2x Cos 23 find diy %3D

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Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

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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: 6. Find the general solution of (D²+D)y=sinx.

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Q: Find the value of zr» at the point (0, 3, 2) where a²y² + 2² – cos(ryz) = 10.

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Q: 11. y= e4x %3D 2x 12. y= e cos 3x

A: We can solve this question using chain rule and product rule of derivative.

Q: Find 2: (a) y = cos(1 1x + 5x)

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Q: 3. у" — у' — 2у %3D5 sin x y(0) = 1, y'(0) = -1 -

A: