Exercise 5. Let z=x+iy be a complex number such that cos (3z) # 0. Then Re(tan(3z)) is equal to sin3xcos3x a. sinh23x+cos²3y sinh(3x)cosh(3x) b. cos2(3x)+sinh²(3y) sin(3x)cos(3x) с. cos2(3x)+sinh²(3y) d. None of these

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

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Q: Evaluate the integral: cos 4x cos 6x dx. A) sin 2x + sin 10x + c. 20 -sin 2x + sin 10x + c. C) sin…

A: Let's find integration of given function.

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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…

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Q: Step by step

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Q: 1 y = e*(C, cos2x + C2sin2x) –xe*sin2x a. 2 b. y = e*(C, cos2x + C2sin2x) +xe*sin2x 1 y = e*(C,…

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Q: Find z in 2= Sinh (4-j5). cos (4-5) express in polar porm

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Q: Consider the following IVP: у" + у'%3D -сos x; у(0) %3D а, у'(0) 3b Find the general solution. 1 1…

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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

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A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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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: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

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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: Solve the integral / cos 10x de 1 sin(10x) + C 10 sin(10) + C 1 ·cos(10x) + C 10 1 sin(10x) + C 10…

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Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: 4) Exercie S Hst 2x+iy be a complex mumber such thet (-s(37)#0Then Re (tent3z))|c equal to: Sin Bx…

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Q: 11.1.5 Show that (a) cosx = Jo(x) +2(-1)" J2n (x), n=1 (b) sinx =2)(-1)" J2n+1(x). n=0

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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: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

A: We have to use derivative definition.

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

A: In both solutions i have used the definition

Q: 3. у %3D С1 е2х sin3x cos3x + c2 e²x

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Q: 2) Find all solution of the equations in the interval [0,2x]. a) 2sin 30+ 12 = 0 b) (cosx- 1)(sin x…

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Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

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Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

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Q: Evaluate: Scos 2xdx cos2x, cos 2x +C A 2 6 sin2x sin32x +C 6. B 2 cos2x cos 2x + C 6. 2 sin2x,…

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Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: The suitable substitution to evaluate the integral cos°(2x) dx is 5(2x) 3 csc°(2x) u = sin(2x) u =…

A: First, simplify the integrand and use the substitution method

Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

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Q: Evaluate the integral. 1/2 |[cos 9t i- 3 sin tj + sin? 3t k] dt T/2 | (cos 9t i- 3 sin tj+ sin 3t k]…

A: We have function ∫0π2r(t) =∫0π2[cos9t i -3sint j + sin23t k ]dt

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: 5) Evaluate the real integral 27T 1 de (5+ 3 cos 0)(13+5 cos 0) by complex variable methods, i.e.,…

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Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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Q: 1-Find the Cauchy principle value (showing details): J_co (7*+5x²+4)' cos(4x) dx 8.

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Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: I. Fill the table in. CN Z1 Z2 No. Rec Pol Exp 1. 5- j5 2. 152-34° 3. Z3 25ein 4. Z4 -13-j12 5. Zs…

A: Since you have asked multiple questions, we will solve the Q.8 and Q.9 for you. If you want any…

Q: Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

A: solution

Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: Substitute the expressions for u and v in the integral. (글sin(| ») - / ÷a x cos 7x dx = sin( |x) dx…

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Q: Let z=x+iy be a complex number such that coshz =0. Then Im(tanhz) is equal to * sinycosy…

A: first option is correct answer. Thankyou

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,

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°.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.