Which of the following is the length of the polar curve r = 0 , 0<0 <1? V2 – In (v2+ 1) 2 V3 – In (V3+1) - 2 1+ In (V2 + 1) V2 + In (v2+ 1) 2 V3+ In (v2+1) 2

Q: 2 7 Find the projection of v = -1 onto the line tlof R'Igiven by the parametric equation e = tul…

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Q: Find the exact length of the polar curve. r = 0, 0 < 0 < 37/2 12.47776

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Q: Consider the following. C: line segment from (0, 0) to (2, 4) (a) Find a parametrization of the path…

A: Given- C: line segment from (0, 0) to (2, 4)

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 0…

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Q: Let w = 8y dx+ 8x dy+ dz be a one-form on R³. Find a parametric curve a : [0, 1] → R³ such that w =9…

A: The line integral ∫CPdx+Qdy+Rdz involves integration over a specific path. The general form of the…

Q: compute the length of the polar curve. The length of r = θ2 for 0 ≤ θ ≤ π

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Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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Q: 2. Consider the circle C₁ : r = 1 and the roses C₂: r= cos 20 and C3 : r = 2 cos 20, each of which…

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Q: 3.4.6 Use Green's theorem in a plane to evaluate the line integral 110²-35²) x + ( [(e¹-3y²) dx +…

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Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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Q: Find the exact length of the polar curve described by: r = 5e 7 on the interval 2 0.000118

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Q: Show that r = fi(0) and r = f2(0) define the same curves %3D in polar coordinates if f1(0) = – f2(0…

A: Given, r=de1-ecosθ, r=-de1+ecosθ define same curve r=f1θ=f2θ show that  f1θ=-f2θ+π…

Q: 6. Find the projection of v = | -7 onto the -2 line l of R given by the parametric equation l = tủ,…

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Q: Find the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.

A: Given:        r=2sin3u3,  0≤u≤3π

Q: A Cartesian equation for the parametric curve x=24sin?e, y=21cos20, n ses 31/2 is given by O…

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Q: The length of the polar curve r = e80/15, 0 <o s T; т is given by -(ešT/15 – 1), where m and n are…

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Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of e…

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Q: Consider the curve given in polar coordinates by r = 0 + cos 0 . Compute the slope at 0 = 0. %3D O…

A: Slope of polar curve r=f(theta) is given by dr/d(theta) Differentiating r with respect to theta we…

Q: Y=V Cos 2O

A: The given function is, rθ=cos2θ The interval of θ is 0, π4 The axis of rotation is y-axis To find…

Q: - 4. Let w = 3y da + 3x dy + dz be a one-form on R°. Find a parametric curve a : [0, 1] → R° such…

A: Given: Let us consider the given w = 3y dx + 3x dy + dz be a one-form on ℝ3 and determine a…

Q: Let w = 8y dx + 8x dy + dz be a one-form on R3. Find a parametric curve a : 0, 1] → R³ such that W =…

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Q: Prove that the curve y:(-,) → R³ is regular with factor H and determine whether the image y (t) = (2…

A: To determine : the      included in a plane in   or not. Here,…

Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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Q: 2. Consider the circle C₁ : r = 1 and the roses C₂:r = cos 20 and C3 r = 2 cos 20, each of which is…

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Q: -2 Find the projection of v = 1 onto the line l of R³ given by the parametric equation l = tủ, where…

A: We will find out the required projection.

Q: Find the length of the following two-dimensional curve. π 3 r(t) = (3 cos ³t, 3 sin ³t), for Osts- 4

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Q: Consider the polar curves C1 : r = 3 – 2 sin 0 and C2 : r = 4sin 0. Let A and B be the points of…

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Q: a) Compute the enclosed area and length (from 0 to 2pi) of the parametric curve given by 3, 3, x = A…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: Find the points of horizontal tangency to the polar curve. r = 3 csc 0 + 5 0 < 0 < 2n (r, 0)…

A: Solution:- Given,  r=3 csc θ+5    0≤θ≤2π To find Horizontal tendency, find horizontal tangent lines…

Q: Find the exact length of the polar curve described by: r = 5e-0 1 on the interval T <o< 9n. 10

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Q: Q1/Prove that the polar expression for the function y = Vx2 - (x2 + y²)3/2 is r = cos20 Q2/Find the…

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Q: Calculate the slope of the polar curve  r=4cos3θ  at the point where θ=5π/6

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Q: Consider the graph of a polar curve in the r0-plane plotted only from 0 = 0 to 0 = 27/3. Plot this…

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Q: Consider the polar curves C1 : r =  4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2)  cos θ as shown in…

A: Given: C1:r=4+322cosθ  C2:r=2−222cosθ To find: a) Area b) Perimeter

Q: Identify the symmetries of the curves in. Then sketch the curves in the xy-plane. r = 1 + 2 sin θ

A: Explanation:  Given that equation of the curve:                             Check the symmetries…

Q: Consider the polar curves Cı : r = 3 sin 20 and C2 : r = 3 cos 0, and let R be the shaded region as…

A: It is known that sin2x=2sinxcosx. Using the zero factor property, it can be written that: if ab=0,…

Q: 2. Consider the polar curve r = 0² + cos(0) where 0 < 0 < 5. Which of the following values of 0…

A: note : in polar coordinate r=k , where k is a constant , represents a circle of radius k centered at…

Q: Find a parametric representation = z(t) for the upper half of = Z Iz – 4+ 2i| = 3.

A: Given to represent parametrically z=zt for the upper half of  z-4+2i=3 Let z=x+iy Then the equation…

Q: Find the polar eauation for the curve represented by the given Cartesian eavation. Dy=-4x² 1.

A: We need to find polar equation.

Q: Consider the conic below a2 + 4xy+4y² – 2/5x + V5y = 0 and determine what is asked. 1)…

A: If we have a rotated conic with the general equation: Ax2 + Bxy + Cx2 + Dx + Ey + F = 0, then, we…

Q: Prove that the function U(r, 0) = tan- ( ), 0<r<1,0 s0< 2n is harmonic inside the circle Iz| 1.…

A: Given Ur,θ=2πtan-12rsinθ1-r2, 0&lt;r&lt;1, 0≤θ&lt;2π---1. The Laplacian equation in polar…

Q: Prove that any polar curve r= f θ with the propertythat the angle ψ between the radial line and the…

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Q: 3. Find the exact length of the parametric curve x = sin-1t, y = In /1 – t2, 0<t<

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Q: 6. Find the projection of u = -7 onto the -2 line e of R given by the parametric equation l = tũ, -1…

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Q: Consider the polar curves Cı : r = 1+ cos 0 and C2 : r = 2 cos 0, and let R be the shaded region as…

A: Integral