) Evalmate f (67 6+24/dx+ (57-34y )dy whore Ca the ellpse 97²+y2=9Also expha. Green's Theorem in vertor notation. Page No. EAGLE Teacher's Signature.

Q: What shape does the graph of r = 1+2 cos 0 take? Circle Cardioid Lemniscate Rose Leaf Curve O…

A: Given: r=1+2cosθ To determine: The shape of the graph of the given function.

Q: Miscellaneous Operation on Complex Numbers 1.42+

A: 1. Given,          42+i

Q: Given u=y3-3x²y is harmonic, find harmonic conjugate - 3.xy2 +x² +c - 3xy2 –x³ +c - 3x?y² +x³ + c -…

A: please see the next step for solution

Q: Which of the following integrals will yield In u+ C? A. SE B. S- x+1 D. S dx xdx C. S 2rdx = x+1 O…

A: From the following integrals will yield ln u+C Note:     Multiple questions are given, we are answer…

Q: Practice by Evaluating 1 VI-x² cos(a² + y³)dydx 0.

A:

Q: Find the harmonic conjugate of the following. Show complete solution.

A: Given,             ex2-y2cos(2xy)

Q: Roll a die twice and observed₁ and 2. (a) Find S. (b) A: X₁ + X₂ = 4, Find the elements in A, and…

A: GIVEN:  Roll a dice twice X1:number on first roll X2:number on second roll

Q: Denive the reatonship betwen B an u = Bsn (ut +ø) and u = A, Cosut + A, sinut n4o and A, andA in

A: Use the trigonometry identities and simplify the second expression and compare with first one.

Q: 4. Find the exact value of cos *x- sin "x-cos (2x). 4 cos x- sinx- cos (2x) = (Simplify your…

A:

Q: 4. (a) Let u be a harmonic function in D. Show that if v is a harmonic conjugate of u in a domain D,…

A: Given: u is a harmonic function in D. v is harmonic conjugate of u in D. To show both u2-v2, u3-3uv2…

Q: Question 6 |5x sinx dx = 5x cosr +5 sinx +c OA. 5x cosx -5 sinx +c В. OB. -5x cosx +5 sinx +c Oc.…

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Q: cos I+1 dx cos²x

A: Solved below

Q: 1 If x= tand , then dr coso do . (1+x²) ½° A True B False

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Q: Find +he obmain ond rage of the hallowing functions 1 i) Cos(x-T) ii) x²+x-2 iii) Lan:

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Q: Let ( A) D = and BD= . Find the angle between BD and A D* O [cos] 2/N(30(21)) O [cos] (-1)…

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Q: e) lim 1-cost sin²)

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Q: Multiple choice. Part D. d 2 √x sin ²x + 1 + √(1-x²] dx (A) arcsin x (D) — arctan x (B) arccos x (E)…

A:

Q: Q3: Find the general solution of the given differential equation: у" + 3у" — 4у%3 0

A: Ode

Q: Evaluate the following.

A: Given that : The integral is ∫ cos β ( 1 - cos 2β)3 dβ .

Q: 1 5. Find lim 2+sin 0 2 sin 0

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Q: %3D Hads findl the unib nomel and the binomd veitor ,F (H)= CamScanner Ligió ä> gus

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Q: Find the derivgtive of the functin. Do nut Simpluy The answer y= tan (1²) arc Sin (1-x)

A: Find derivative

Q: f cos 0 = where <0 < 2n and tan 3= where r < B < , set up the triangles that represent each trig %3D…

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Q: Identify the symmetry in the graph of (a) r = 4 + 4 cos θ and (b) r = 4 sin θ.

A: Given  (a) r = 4 + 4 cos θ and (b) r = 4 sin θ.

Q: TT de 21. Evaluate f" by using the Residue Theorem. 3+cos 0

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Q: MAT441 CALCULUS II – PROJECT #5 Evaluate S cos (3x) dx. √√4 - sin² (3x) Answer. Step 1: Exercise 1

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Q: Question 2 Q1B Fill-in the blanks with the correct letter of the answer from the given choices. 7(2+…

A: