(1 point) Suppose that C is the curve defined by the polar equation r = 2 +4 cos 0 (called a limacon). Suppose the integral v20 + 16 cos 0 d0 computes the arclength of the inner loop of C, where 0 < a < b < 2n. Find a and b.

Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos at…

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Q: Find the derivative dydx of the polar function r=1+sinθ at θ=π4.

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Q: Give a rough sketch of the graph of the curve r= 1+ cos40, 0 < 0<2r.

A: The given curve is  r=1+cos 4θ,  0≤θ≤2π

Q: Show that the polar equation for x2/a2 + y2/b2 = 1 is                                           r2 =…

A: Plug x=rcosθ and y=rsinθ

Q: Draw the polar curve r = cos(30) with its orientation. Set up all integral to evaluate the length of…

A: First, find the node to the polar curve by equating r = 0, so cos(3θ)=rcos(3θ)=0(3θ)=-π2,π2θ=-π6,π6…

Q: Consider the polar curves C1 : r = −3 sin(2θ) and C2 : r = 3 sin θ. 1. What is the equation of the…

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Q: 3. Find the polar coordinates of all points on the cardioidsr=1- sine, at which there is a…

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Q: Find where the polar function f (theta) = 6 cos(theta) has a vertical tangents over [0,2pi]

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Q: Graph the polar curve r = e® for 0< 0 < n.

A: The given polar curve is,

Q: 7. Find all points of intersection of the r= 3sine polar curves: such that r= 1+sine

A: We equate the two equation to find solutions.

Q: Find the equation of the tangent line to the polar curve r = 3 + 8 sin θ at θ = π/6. Note that…

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Q: Determine the arc length of the curve formed by the polar equation r = 4 cos 0 - 4. 2T 2п 2√/2 √1 -…

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Q: Sketch the graph of r = a(1 – cos8) In polar coordinated , assuming a is a positive constant Is 2.…

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Q: 3. Write down the name of the conic given by the polar curve r = 6/ (2 - sine). Determine the…

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Q: 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.

A: Any point on the Cartesian coordinate system is represented as x, y. Any point on the polar…

Q: For a &gt; 0, a lemniscate curve is the set of points P such that the product of the distances from…

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Q: 3) Use polar coordinate to evaluate S'S_√x² + y² dxdy.

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Q: b. Plot the polar curve r= 2(1- cos0) in interval t ,2n

A: Given equation is r=2(1-cosθ)  =2-2cosθ