Give examples of four-leaved rose, lima ̧con, lemniscate, cardioid in polar coordinates. Sketcheach of them. And find the closed area that are enclosed by each of them.

Q: Sketch the set of points (described in spherical coordinates). ρ = 4

A: Sketch the set of points (described in spherical coordinates). ρ = 4

Q: Find the points at which the polar cone irc4coso, has horizontal and vertical tungent liner.

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Q: Sketch the segment r = sec 0 for 0 < 0 < . Then compute its length in two ways: as an integral in…

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Q: Explain why in spherical coordinates the graph of = c is a half-plane and not an entire plane.

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Q: change from.polar to Cartesian Lo-ovdinate's (1,0) :- -: : . (3, 7), O (1,) © (-4, ),@ (5, n

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Q: Which of the following is the surface area of the solid body created by rotating the given…

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Q: Evaluate the given Mtegral y ehanging f2x°ydĂ, uneve O is the top half of the disk the polar…

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Q: Describe the given region in polar coordinates.

A: Given,

Q: Evaluate Z in polar form In [cot(4e13)] Z = j4

A: The given problem is evaluate and simplify the given complex expression and express in the polar…

Q: Graph the surface whose spherical equation is p = 1– sino.

A: We use maple software to graph the given surface.

Q: 20) Find two sets f polar coordinetes, (r, o),0LOL2 IT Por the point (6,6) in recten- gular…

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Q: How do you find the area of a polar regionR = {(r, θ): g(θ) ≤ r ≤ h(θ), a ≤ θ ≤ β}?

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Q: Convert the following quadric surface into spherical coordinates.

A: Convert the quadric surface into spherical coordinates.

Q: Draw the polar region {(r, θ): 1 ≤ r ≤ 2, 0 ≤ θ ≤ π/2}. Why is it called a polar rectangle?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

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: 3) (2) 2 3 元16 2 " 11元 6 57元 6 3 2

A: We have to plot a given point in the graph.

Q: If a point is represented as (x,y) in the Cartesian plane and (r,0) in the polar plane, then 0 = tan…

A: A point in cartesian plane is (x,y) and (r,θ) in the polar coordinate, then θ=tan-1yx.

Q: Find the area and points of the intersection of the regions enclosed by the r = 2 and r = 3 − 2…

A: We have to find the area and points of the intersection of the regions enclosed by the r = 2 and r =…

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: duct z,z2 and the quotients 1 and (Express your answers in polar form.) Z2

A: We will solve the problem on complex numbers.

Q: What is the minimum angle of rotation (in degrees) that will carry the six-sided star onto itself: I…

A: It is a 6 sided star that means it will redivided into 3 parts:⇒ we divide 360°( full rotation ) by…

Q: Circle to the center of C is a origin Coordina tes and radius 4

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Q: Use polar coordinate system to sketch and find the common arear = 2+ 2cos0 and x2 + y2 = 1.

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Q: Write down the parametric equetions |3D 4=6-t in cartesion Form

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Q: the polar coordinates to find the volume of a sphere of radius 1. -

A: Given;  Sphere of radius 1.

Q: Graph the polar curve using Desmos.com, and find the area enclosed by one loop of this pol curve: r…

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Q: 3. Infer some rosults from the axioms and illustrations of the three- line and four- line…

A: As per your requirement, answer of 3rd part is mentioned below

Q: Explain why the element of area in Cartesian coordinates dx dybecomes r dr dθ in polar coordinates.

A: the integral which is used to find the area in cartesian coordinates is  ∫Df(x,y)dxdy…

Q: Find the area of the rigion lies between the circles r=2 and r=4cos(theta) in the first octant.

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Q: Find the number of points of intersection of the polar curves r=2cos0 and r=1+2sin0. O 1 3 O 2

A: Number of point of intersection of polar curves r=2cosx and r=1+2sinx

Q: area of one loop

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Q: find the area of the Shaded Part AUsing Polar y =2X

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Q: Find the the area of the region enclosed by the polar equation r= 3sin(20), 0 < 0 < 1/2. 3.

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Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec θ

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Q: Graph the 2 polar curves and then write an expression involving at least one integral that…

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Q: Illustrate what are the intersections of polar curves?

A: Question- Illustrate what are the intersections of polar curves? Answer- If the equations are…

Q: Fxx) = - + Show that Fis Conservative. Compute S . di where c, is the Unit Circle ceintered

A: If    F→x,y is conservative vector field  then its line integral along any closed path is Zero , ie…

Q: Usmg panametric equahons in pOlar coordmates to shav that the surface area of a sphere cantered at…

A: Use the parametric equations in polar coordinates to show that the surface area of a sphere centered…

Q: yepriate trigonomic subititution to rewrite the intya) U se in the form E sec'e de

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Q: Describe in polar coordinates the region in the first quadrant between the circles of radius 1 and…

A: The Polar equation of a circle of radius 1 and having center at the origin is: r = 1

Q: Identify the surface whose equation in spherical coordinates is given by p = 8 cos %3D

A: The given equation in the spherical polar co-ordinates is ρ=8cosϕ. In spherical polar co-ordinates,…

Q: Is the formula for area in polar coordinates valid if f (θ) takes negative values?

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Q: Show that Jac(G) = ρ^2sin φ, where G is the map for spherical coordinates given by G(ρ, φ, θ) = (ρ…

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Q: Evaluate ds where C is the upper half of the circle centered at the origin with radius 1 with the…

A: Draw the curve C:  Here, we divide C in two parts:  C1 represented by the curved part C2…

Q: Find the area shared by the circle r,= 10 and the cardioid r, = 10(1- cos 0). %3D

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Q: Find the length of and the area enclosed by the polar curve r = sin(2θ) + 1.

A: Given  The polar curve r = sin(2θ) + 1.   Formula :- Arc length of the polar curve  L=∫αβr2+drdθ2dθ.…

Q: Describe in polar coordinates the line segment that has "(x, y) = (3, 1)" and "(x, y) = (6, 2)" as…

A: The cartesian to polar form can be written as: (r,θ) Where, r=x2+y2 and θ=tan-1yx

Q: Find the areas of the regions Inside the six-leaved rose r2 = 2 sin 3θ

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Q: Find area of the region bounded by the following polar curves.

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