2.3 Evaluate the integral sinh 2 dz, 7 3i (z – 2i)4 2i 2+ 4 where C is the circle |z – 2i| = 4 traversed once anticlockwise. State clearly which results you used to arrive at your final answer.

Q: 4] [2M] Evaluate the iterated integral o So V sin(x2 + y? )dx dy by converting to polar coordinates.

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Q: 27. Inside the circle r = 3a cos 0 and outside the cardioidr = a(1+cos 60), %3D %3D a > 0

A: Find the area of the region inside the circle and outside the cardioid, where the equation of circle…

Q: Evaluate the integral sinh? z + z+4 3i dz, (х — 21)4 - 2i where C is the circle |z – 2i| = 4…

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Q: ● Evaluate the following integrals: 4 Convert this Cartesian equation (x² + y²)²_9(x² - y²) = 0 to…

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Q: If y = cos ¹ prove Zyy + z = 0. )Z = (1 + i)(2-1)-¹, find |Z|.

A: Here given y=cos-1(z/x). We prove that zyy+z=0.

Q: Find the length of the path for c(t) = (4(0 – sin(0)), 4(1 – cos(8))) over the interval 0 < 0 < 2r.…

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Q: find area Inside the oval limaçon r = 4 + 2 cos 0 Inside the cardioid r Inside one leaf of the…

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Q: r(t) =(sin 3t, cos 31, V7t), 1. Let a) Find T(t) and N(t)

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Q: 21. ds: C is the quarter-circle r(t) = (2 cos t, 2 sin t), for 0SIS#/2.

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Q: The positions of two particles on the s-axis ares1 = sin t and s2 = sin (t + π/3), with s1 and s2 in…

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Q: e'ス+×cos(2) 3. (o'1'e)と Flsye)-xをえゃxそsQe)s Find Curl at

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Q: 4.3 Use the calculus of residues to evaluate the following integral r27 1 d0. 1+8 cos? 0

A: We find the given integral by using calculus of residues.

Q: and casy=0t, and DLyr, Furd the exact alue of tan Ca-y.

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Q: f arctan y dy 3 ¥

A: Given problem:- ∫arctan(y)/y3 dy

Q: 5. Let y (sin(2r)) (nz). Find 2. Express your answer only in terms of r.

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Q: 5. DETAILS SCALCET9M 14.5.015. az az and as at Use the chain rule to find sin(8) Z = r = st, 0 = s3…

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Q: 8. Find the length of the given curve over the indicated interval. r(t)= (r', 3 cos(t), 3t) [] 0, 2

A: Given r¯(t)=t2,3cost,3t in the interval [0,π2]

Q: Match the graph to the equation. I T 37 47 5n 67 7n 8n 9n 10n11n 12n -1 -2 -3 -4 -5 O y = 4 cos - 1…

A: At  θ = 7π y = 4 cos (θ/4) - 1  y = 4 cos (7π/4) - 1 y = 1.82 which satisfy the graph value of y

Q: 4. Evaluate the following and give the exact value: - Tt/4 r2 cos 0 crsin 0 r2 cos 0 dz dr d0 0,

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Q: 6. Find the solution to the following IVP. (a) r- 2y = x sin (2r) – r³ + 4t, given y(n) = . %3D

A: Given equation: xdydx-2y=x5sin(2x)-x3+4x4 Condition yπ=3π42.

Q: The region inside the rose r= 2a cos 20 and outside the circle r = av2.

A: The given equation are  r= 2acos(thitha) r=a√2

Q: 1) 土七 COS ant5 Sinant3 an: 2then fird the m lim 3) D. Ehmit does not exist

A: Given query is to find the limit of the expression.

Q: 9. Find the length of the curve: r = 1+ cos(20),0 < 0 s 2n

A: given equation of curve r=1+cos(2θ)   , 0≤θ≤2π as per our guideline, we are supposed to answer the…

Q: 13.2. Find the length of the arch of the cycloid given by z(t) = a(t – sin t) + a i(1 – cos t), 0 <t…

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Q: 5. Suppose that u is a harmonic function in the disk D = {r< 2} and that u = sin 30 – 2 cos 30 + 4…

A: Given: The given harmonic function u=sin3θ-2 cos3θ+4 in the disk D=r≤2 for r=2.

Q: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t = 2n. %3D 2. Find the length…

A: As we know that, The expression for the length of vector-valued curve is: L=∫abx't2+y't2dt   1).…

Q: G:2 Approximate the sel of K= Sin xo upto 4 decimal places by using Nedu'ton methed

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Q: 1) Let 7(t) = (t, 2 cos t, 2 sin t), -4 <t< 4. Find the length of the curve.

A: In

Q: A standing wave on a 2-m stretched string is described by: y(x,t) = 0.1 sin(2rtx) cos(50tt), where x…

A: Solution :-

Q: For the following, use the information provided to solve the problem. (7) Let w(x, y, z) = xy cos z,…

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Q: 21. ds: C is the quarter-circle r(t) = (2 cos t, 2 sin t), for 0SIST/2.

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Q: 1.Why does the following DE have an unique solution on an open rectangle that contains the point (O;…

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Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 1+8 cos? 0

A: We have to solve the integral by residue formula

Q: Determine the value of k which will make h' (7/4) = 6 when h(r) = ln (cos z) + kr. %3D O 5

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Q: Q:9 Evaluate cot(72)\dz 3 [z e? + by Cauchy's residue theorem.

A: We have to solve the given integral by Cauchy residue theorem

Q: Q2// I= f, (x² cosx) use Simpson's 1/3 rules, with n=4.

A: We have to find the integral using Simpson's 1/3rd rule. In first question there is not equal…

Q: Given x(t) = Acos (120 + p) = A1 cos120t + A2 sin120t. Find A1, A2, A and o when x(0.1) = -0.995 mm…

A: There is a typing error in the question. We have solved the question after rectifying the error as…

Q: If P = 2 sin(10t + x − π/4)ay and Qs = ejx (ax − az)sin πy, determine the phasor form of P and the…

A: Given- If P = 2sin10t + x - π4ay and Qs = ejxax - azsinπy To find- Determine the phasor form of P…

Q: 7. Find the area of the region that lies inside both of the circles; [Ans: }( – 1)] r = 2 sin 0, r =…

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Q: Show that the tollawiny ey uation has a solution 9(4) 5.t lim y 4)=9 そ-3 I y't (cos?t) y't (sin t) y…

A: Given equation is y''+cos2ty'+sinty=0 It is a homogeneous differential equation of second order. The…

Q: A T 3n 4n Sn 6 7n 8A 9n 10n11n 12n Match the graph to the equation. 4 cos -1 O y = 3 sin - n) - 1…

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Q: Suppose that the volume, V, and radius, r, of a sphere are changing with respect to time and satisfy…

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Q: 7. Find the length of the curve: r = 1 + cos 0

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Q: 4.3 Use the calculus of residues to evaluate the following integral 2m 1 de. 1+8 cos? 0

A: We find the given integral by using calculus of residue.

Q: 2 Without using technology, sketch the graphs of the following for 0°<x < 360 a y = sin æ + 1 90 180…

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Q: If r(t) = (VE – 1, ln(10 – t), sin(2t)) then the domain of r is

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Q: By about how much will h(x, y, z) = cos (paixy) + xz2 change if the point P(x, y, z) moves from…

A: The given function is,

Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

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