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: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: Find all harmonic conjugates of u(x, y) = x³ - 3xy² + 2y.

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Q: FCx): 2x-5xナ3 find f'co).

A: We are solving the first question and for the next question post the question again and also mention…

Q: The general solution of (D2-2D+1)y=2sin x A y= ce*+c>xe* + sinx B y=ce*+c2xe* + sinx+cos x…

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Q: (D² - 4D + 5)y = e*; y a. y= e²*(C,cos2x + C,sin2x) – –e 10 b. y e2*(C,cosx + C,sinx) +e 10 C. y =…

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Q: Q1) L-¹ (²-1) = a) cosht -1 Q2) The general solution of y"" + 2y" -y'-2y = 0, is: 2x a) y(x) = c₁e²x…

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Q: W = spanR{1, cos² (x), sin² (x)} = R + Rcos² (x) + Rsin²(x) Justify for each of the subsets {1, cos²…

A: Given: W=spanℝ1, cos2x, sin2x=ℝ+ℝ cos2x+ℝ sin2xWe need to justify for each given subsets that it is…

Q: D) Factor f (x) = x³ + 2x2 + 4x +8 into complex linear factors. %3D

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Q: f(i) = 5, f'(i) = -3i, g(i) = 3i, and g'(i) = 4. Find (fg)'(i).

A: Given fi=5,f'i=-3i,gi=3i,g'i=4. Find fg'i.

Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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Q: Let f(x)=sinx.When x=and dx=,then dy=? a) √2 b) cosxdx π+2 c) sin (+²) - sin() d) √2 √2 con()+sin()…

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Q: find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0,…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: 8 410x-32+x2 cos2x 4 Find *: (a) y =

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Q: Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to…

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Q: Use an appropriate substitution to integrate 2. A sin u +c 12r'sin (x?– 2) +c © 12sin (x2- 2) +c…

A: To evaluate the given integral.

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

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Q: how

A: Que seems some data missing. Though I have simplified the given expression as much as possible.…

Q: (D³ - 3D2 + 9D + 13)y = 0

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Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

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Q: z.e +4 a'z cos(2x+y) z.e Solve ax 4 əx-əy axəy

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Q: ution t= tan 2 tan). os(x)

A: We have to choose the correct answer from the given option

Q: lim

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Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

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Q: Evaluate _i(z³+i³) 2 z +1

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Q: (D2 -4D +7)y = 0 A y = e²"(c,cos/2x+c,sin/2x) COS y = e2"(c,cos/3x+c,sin/3x) В © y = e (c…

A: 1. Given differential equation is (D2-4D+7)y = 0 Here Auxiliary equation is D2-4D+7 = 0⇒ D = 4 ± 16…

Q: Calculate facos xdx . (a) rsinr – casz+c (b) Icosz+sin x+c (c) zcost-sin x+c (d) Isinz+cOSI+C (e)…

A: Formula for integral by parts :        ∫u(x).v(x) dx=ux∫vxdx - u'x∫∫vxdxdx+…

Q: 6) Use Linear Property to find ( 1- 3 x4)' A) (1- 3 x4) %3D B) – 4x3 C) - 2 D) - 12 x3 7) Use…

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Q: Solve y = x - 2ycot2x A B (C) D 2xsin 2x + (4y - 1) cos2x = C (4x - 1) sin2x + 2xcos2x = C (4x − 1)…

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Q: z is a complex variable z=x+iyFind all points of discontinuityf(z)=(3z^2 +4)/(z^4 -16)

A: To locate the points of discontinuity of the given function f(z) of the complex variable z.

Q: f'(3i) = -i, g(7+ 2i) = 3i, g'(7 +2i) = -4. Find (f o g)'(7+2i). 4i -4i 2.

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Q: (x² + 1)ª (2.x + 1)3(3x – 1)5 y =

A: Simple differentiation problem....

Q: (D4 + 18D2 + 81)y = 0 (A y = (c, + c,) cos3x + (c,+c,) sin3x. (B у %3 (с, + сх) cos:3x + (с,+c)…

A: To solve the given differential equation first we construct auxiliary equation and then solving the…

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A: We will use concept of arc length in 3d We want to determine the length of a vector function,…