Convert to polor coordinates with  r ≥ 0 and 0 ≤ theta < 2pi (4,0)  (r, theta) = ?

Q: For long cirular cfinder of Re two halves maintained at temprature U1 and Vi respectively, Show that…

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Q: Find Equatien of the tavgnt lin tu th cuve at tk giver pointe y= sec X ,

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Q: Find the solutiTon of followina ordfnarg differentral equation -2x

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Q: Consider the helix r(t) = (cos(4t), sin(4t), –2t). Compute, at t

A: Compute unit binormal and curvature at t=pi/6

Q: Use Green's Theorem to evaluate (sin r + y) dr + (cos y +a?) dy, where C is the square con- sisting…

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Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

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Q: he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

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Q: Find the area outside "r^2=9cos(2theta)" and inside "r=2-cos(theta)"

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: Evaluate the 2 intergrals attached as images with the question.

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find the length of the cardioid r = 1 - cos θ.

A: Arc length in polar coordinate is given by:

Q: Sketch the solid described by the given inequalities: 0&lt;=r&lt;=2, -pi/2&lt;=theta&lt;=pi/2,…

A: First draw the first two inequality 0&lt;= r &lt;=2 and –pi/2&lt;= theta &lt;= pi/2 in the…

Q: 01: Find the angle () between the tangents lines of the 3 sec 0 and the cardioid r 4(1+ cos 0) at…

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Q: Find the length of are リ-Jx-2+ Sa'z) + Sin

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Q: 01: Find the angle () between the tangents lines of the 4(1 + cos 0) at the line r 3 sec 0 and the…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: Calculate the area of the circle r = 3 sin θ bounded by the rays θ = π/3 and θ = 2π/3.

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Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Find the length of one arch of the cycloid 2(t – sin(t)), y = 2(1 – cos(t). х

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Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: isfies the differ and the auxi

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Q: cos(x) dx

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Q: Given the cardioid r= 3(1+cosθ) 0 ≤ θ ≤ 2π Determine in wich points the cardiod has vertical…

A: Differentiate the equations r=31+cosθ and x=rcosθ with respect to θ, to find drdθ and dxdθ.…

Q: Find the length of one arch of the cycloid 8(t – sin(t)), y = 8(1 – cos(t)). %3D

A: Given: x = 8(t -sint(t)) y = 8 (1-cos(t)) To find the length of arc.

Q: Find the conjugate harmonic of v(r,9) = r² cos 20-rcose+2. Show that vis harmonic.

A: Given vr,θ=r2cos2θ-rcosθ+2

Q: Find the length of one arch of the cycloid = 5(t-sin(t)),y- 5(1-cos(t)).

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Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

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Q: What is the radius of the given contour |z + 2i| = 8 + 7, 0 s 0 s 2n ?

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Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: The equation of the tangent plane to the surfice. -yeV + = 0 at the point (0,1,1) is ar + by + cz =…

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Q: Verify the formulas d u' -[arcsin(u)]: dx Vi-u d u' -[arccos(u)]=- dx V1-u? d -[arc cot(u)]= dx u'…

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Q: Integrate counterclockwise around the unit circle (|z| = 1) and choose from the options below that…

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Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: Find the mibimal distance between the foint Cl,4) to the linz Yeメtl. dっしくーメュ+(-

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Q: Find the length of one arch of the cycloid x= 5(t-sin(t)), y= 5(1-cos(t)).

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Q: Find the concevity. point of infleetion, of fluj n=770 Also explain it jeometrically

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Q: Use Green's Theorem to evaluate 5x*dx +xydy where C is the triangle with vertices (0,0), (1,0),…

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Q: What is the integrating foc tor of the equation %3B

A: Topic:- differential equations

Q: Find an equation for the tangent plane to the surface z +4 = ry" cos(2) at the point (4, 1, 0).

A: Use the partial differentiation for finding the tangent plane.

Q: Determine the speed (in meters per second) of a particle with a trajectory (2 sin (3t), 9 cos (3t)),…

A: Consider the given parametric equation of the trajectory of the particle, 2sin3t,9cos3t so we can…

Q: Find the length of the cardioid r = 1 + sinθ

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Q: Find a formula for the distance from the point P(x, y, z) to the xz-plane

A: The distance between two points x1,y1z1 and x2,y2z2: d=x2-x12+y2-y12+z2-z12 The distance from the…

Q: Find the angle in radians between the planes -2x + z = 1 and -ly+ z = 1.

A: See the answer below

Q: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

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