Let R be the region enclosed by the polar curve r (0) = 3 ln (0) where 7π

Q: 1. Let (-V3, –1) be the cartesian coordinates of the point P. Find the polar coordinates (r, 0) of…

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Q: # 3. Sketch the region R inside the curve r = 1+ cos 0 and outside the circle r = 1 and use polar…

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Q: Find a parametric form of the closed curve x? + 2y2 + 2x – 4y – 13 = 0 in the xy-plane with a…

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Q: Find T, N, and k for the space curve, where t>0. r(t) = (8 cos t+8t sin t)i + (8 sin t- 8t cos t)j +…

A: We have given that ,  rt→ = 8 cost + 8t sinti→ + 8 sint - 8t cost j→ + 2k→   ,  where t > 0. We…

Q: Express the region D = {(x, y)|3x² + 3y² ≤ 45} in polar coordinates.

A: D=x,y|3x2+3y2≤45

Q: Use Green's Theorem to evaluate Se (y? – tan-1 (r)) dr + (3r + sin (y)) dy, where C is the boundary…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find T, N, and k for the space curve r(t) = (5 sin t)i + (5 cos t) j+ 12tk. T(t) =i+j+k

A: We have to find  and .

Q: Let f : R²\{0} = {x € R² : x # 0} → R be given in polar coordinates by Cos 20 f(r, 0) = r2 Sketch a…

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Q: The curve C is the circle of radius 5 contained in the plane z 5 and centered around the z-axis,…

A: Solution:-

Q: cos( (a) Evaluate the integral Sp FdA where F(r, y) = and D is the triangle with vertices (0,0),…

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Q: Consider the following two parametric curves in R³: for 0 ¯¯\ND OXO OXO OXO OXÍ These curves…

A: First we will find the intersection point of both server then we will find the equation of potential…

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: 2. Consider the parametric equation r(t) = (1 – t°, t(1 – t)) where –1 <t < 1. (a) Plot this curve…

A: The solution is given as follows

Q: illustrate that the length of a smooth space curve does not depend on the parameterization used to…

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Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: A. Find the linearization L(x.y.z) of the function f(x.y.z) = V2 cos2x sin(y + = (0.0. ). Then, find…

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Q: Suppose C is the graph of y = f(x) for a < x < b. Compute x dy + y dx in terms of f.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the ccw circulation of F = around the curve C: from (0, Guam ( %3D

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Q: B D (4+3+5+2) (1+16+9+25) O (16+9+25+4) 0=1 L 0 T 0 1 ļ 4 ! 3 0=0 3 r = f(0) 5 Let R be the region…

A: Given: In the region R we have, θ 0 14 12 34 1 r 1 4 3 5 2 To Find: The approximate area of…

Q: Consider the polar curve given by r=40' where 0<0<r. Set up, but do not evaluate, an integral which…

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Q: Consider the function f(x,y) over the domain D enclosed by the 1+ x2 + y² polar curve r =2+…

A: (a) Look at the level curves of the function within the domain D.    The boundary of the domain D…

Q: -2y The line integral (e sin x) dx+(x' +3y)dy with path F (t)= (8cost, 8 sint) such that 0sts2n. Set…

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Q: F(x, y) =  (9 y − cos y, x sin y) , and C is the circle (x − 2)2 + (y + 4)2 = 4 (a) Draw the region…

A: Here we are going to solve this using Greens Lemma for Vector Integration

Q: Jo G.dR, where G(x, y, z) = (2x cos (Ty) — 2³, 1 - 7x² sin (ny), 2 – 3xz²) and C Evaluate is the…

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Q: Q Solve the non linear differential eguation )= ex

A: To Determine: solve the nonlinear differential equation. Given: we have an equation eydydx+1=ex…

Q: - Let f(z) = cosh z. (1) Find the image of S := {z = x+iye C: x < 0,0 < y < } under f.

A: Follow the steps.