2 Evaluate each of the following (1)f e 22 dz (2)S zsinz?dz (3) ; z2+1 dz z3+3z+2 -2z 3 Determine poles of the following function and residue at each pole z2 (z-1)(z-2)2 4 Evaluate sinz? dz eG-2) (z-) where C is |z|=1

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A: Given problems:- 5.    y=cos(5x)  6.    f(z) = e5z^2+7z-13 7.   y=4x2+cot(3x)  To find:- Derivative…

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A: For the first question . Option first is correct answer . Thankyou !

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A: A) To prove: ∂f∂x+∂f∂y+∂f∂z=0 Given that u=x-y, v=y-z, w=z-x

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Q: Suppose m and n are constants and m #n. Evaluatesin (mx) cos(nx) dx' cos(m− n)x- = cos(m+n)x] + C 1…

A: Solution is here

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A: Solving

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Q: 15. Suppose that F'(x) = 3x + cos(r - 1) and F(1) = 5. Then find what F(x) is precisely.

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A: we will use following identities to evaluate given expression  a+jb = a2+b2 ∠ tan-1ba and A∠θ1B∠θ2 =…

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A: In this question we will use basic of calculus i.e concept of Rolle theorem. We will use Rolle…

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Q: 5. Suppose that g(r) = f(r) coS I, that f(T/6) = 2 and that f'(/6) = 4. Find g'(n/6). %3D

A: g(x)=f(x)cosx and fπ6=2 ,f'π6=4.

Q: Evaluate Sin (OS - Cos(2x 2. F(Xg.2)2(24-2)で+(2x)デさ(x-g)K C:F(t) = -3€ t+ (2€ + 1) jt4kg ÖZ t<2

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Q: 3 Determine poles of the following function and residue at each pole z2 (z-1)(z-2)² 4 Evaluate sinz?…

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Q: Q3/ Determine: (a) sin(t) .8(2t – 1) (b) (cos nt). 8(t- 1)dt 8(t –

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Q: Evaluate J J-36z² dz 1 sin (5æ) + C 6. O_ 1 -1 sin (6x) + C O_1 sin (5x) + C 6 -1 1 Osin1 (6x) +C 6.

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A: topic -derivative

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Q: 9. The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t tan(x/2)…

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Q: 3. Show f cos2n Ode 277 sin-n Ꮎ ᏧᎾ = 27 22n 11.1 n = 1, 2, 3,...

A: Using Cauchy integral formula.

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Q: 17. (D+ + 2Dz + 1)y = 5– 3x2 a. y = (C, + Czx) cos x + (C3 + C4) sin x – 3x2 + 17 b.y = (C1 + Czx)…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: Suppose m and n are constants and m + n. Evaluate [sin (mx) cos(nx) dx- A) Ⓒ[-(-)-(+)₁]+€ m+ncos (m…

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Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx A − cos(m− n)x+ · -cos(m+n)x] +…

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Q: x+1 Q1/ Prove that coth-1x = x-

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Q: 4. Verify Rolle's theorem in the following cases (a) f(x) = (x – a)m (x – b)", where m and n are…

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