3. Evaluate/calculate using polar coordinates. -1/2 cV1-x² А. M-X" xy/x2 + y² dydx ху,

Q: Q17:- In polar coordinates prove that** 第。

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Q: Find the length of the polar spiral r = 0² from 0 < 0 < V5.

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Q: Write a polar equation of the form r sin(0 – 0,) = ro for the line 2/3 x+2y = 1. %3D

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Q: 2. Compute dy dx (x² + y²)' by first changing it to polar coordinates.

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Q: Transform y = V3'x into polar form.

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Q: Convert the Cartesisan equations x^(2) = 9y and x^(2) - y^(2) =x into polar equations.

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Q: Use polar coordinates to calculate e-(z²+y²) dydx. roo Express -(2²+y²) dydx in terms of dr, and…

A: We will find out all the required values.

Q: Convert to polar coordinates in the xz-plane, similar to Example 3 in the book. r2 63 – 2x? – 2z? –…

A: The limits lead to interpretation that,   From (2), Comparing the above result with  r=3

Q: 1 (x+y')* dy dx -J3X 2

A: Double integration of function gives the area under the function curve. Double integration can be…

Q: 4. Integrate L e-° dxdy by converting to polar coordinates, and ase that result to integrate J e dx.

A: This problem is convert to pollar form and then solve so,......

Q: Convert the Cartesian equation x² + y² -2x= 0 to a polar equation. x2 + y2 -2x 0= O 2=-2 cos e Or= 2…

A: Given artesian equation,x2+y2-2x=0Put…

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² - 4x=0 O A. r cos²0=4 sin…

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Q: 25) Evaluating in polar coordinates: 6*L*(x² + y²)dydx

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Q: Evaluate the by itercated integreal onverzting to polare coordinates. V16-n² 3nd ydn V16-パ 16-42 -4

A: This integration problem is solved by converting rectangular coordinate into polar coordinate

Q: 1. Convert (V3,-3) from rectangular to polar coordinates with r>0 and 0<0< 2r. Give exact values for…

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Q: Use spherical polar coordinates to evaluate LLEN V4-x2 x² + y2 + z² dz dy dx. -V4-x2

A: Solution is given below:

Q: 3. Express the equation y = mx + b, where m and b are constants, in plane polar coordinate.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Write a polar equation of the form r cos(0 – 0,) = ro for the line 3 x- y = 2.

A: Given: To find the polar equation of the form r cosθ-θ0 =r0 for the line 3x-y = 2.

Q: 13 Convert x 2 + y 2 - 2x = 0 to a polar equation. r = 2cosθ r² = 2cosθ r = 2sinθ

A: We have to find the polar equation

Q: 2. Let r>o and Fo tina20 And use polar coordinates KZQ and use polar coordiinates (8,7) >(0,0)

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Q: 2. \ Evaluate •V4-2² dydx + dydx 2x-r2 using polar coordinates.

A: We have to evaluate the integral using polar coordinates.

Q: Q 4/ Use polar coordinate to evaluate 1v1- x2 + y? dydx

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Q: Evaluate by changing to spherical coordinates: /2–x²-y² xydzdydx x²+y2

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Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

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Q: Replace the Cartesian equation with an equivalent polar equation. x2-y2=4 O cos2e - sin20 = 4 O r…

A: 1. x2-y2=42. r2=26r cosθ-6r sinθ-9

Q: Use polar coordinates to evaluate 2/2 dydx. 3 1 0, (x²+y?)? O 5 Оз 6 O 2 O 1 O 4

A: To determine: The value of the integral  using polar coordinates, ∫12∫0x22x2+y232dydx.

Q: 7) Evaluate IT !! (x + y)dxdy y by switching to polar coordinates.

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Q: Transform (0, y) from rectangular into polar form (here y is any negative number).

A: We have convert rectangular coordinates (0 , y) into polar coordinates: Where y is negative number-

Q: (2. Plot the points with polar coordinates 2, and -3, 2 using the pencil. 6. 3 3n 4 5n 6. 4. 7n 6.…

A: topic - plotting of points in polar coordinate system

Q: Write a polar equation of the form r cos(0 – 0,) = ro for the line x - y = v2. %3D

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Q: l+vI+r² xy dydx -z 1-VT-

A: ∫01∫1-1-x21+1+x2xydydxTo transform to polar coordinates and calculate

Q: 1)By the to Pestear Ja-xz changing of the Following double integhals coordinale Polar evaluate (4-y)…

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

Q: What is the zero of polar equation r = 3+2cos(θ)?

A: Given polar equation is: r=3+2 cos θ To find the zero of the polar equation, we must have to put θ=0…

Q: Gz find the Velume of the Selid with in the cylinder xya16 and between the y-2-3 and Z=2(polar)…

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Q: Consider the curve C of equation: (x² + 2y + y²)² = 4(x² + y²). From the following options choose…

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Q: onvert the Cartesian coordinate (4,3) to polar coordinates, 0 < 0< 2n

A: We have to convert the cartesian coordinates (4, 3) into polar coordinates, 0≤θ≤2π.

Q: Evalute the following integrats using Polar method! 2 √4-1² ( x ²³ x ²³ ) d x dy پرشد

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Q: 5. Convert the integral 9-x2 9-x²-y² Vx? + y? + z² dzdydx to spherical coordinates then evaluate.

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Q: Find the corresponding Cartesian equation of the parametric equation       x=3cosθx=3cosθ.…

A: Given:           x=3 cos θ,   y=4 sin θ            0≤θ≤2π From: x= 3 cos θ            cos θ=x3 From:…

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

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Q: 5. Evaluate ffR dA, where R= {(r, y)|1<r² + y² < 9, z20, y 2 0} (Hint: Use polar coordinates.)

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Q: 3T Plot the points with polar coordinates 3, and (2, 2n) using the pencil. 4

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Q: 2. Evaluate Vr2 + y? dy dx by switching to polar coordinates.

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Q: Plot the points with polar coordinates (4, T) and -5, - *-) using the pencil. 2n 3 3n 4 4 6 4 6. 一6

A: Given query is to graph the polar coordinates.

Q: 3. Change (r+1)²+y² = 1 to an equiv- alent polar equation

A: GIVEN (x+1)2+y2=1

Q: 3 V9-y2 / / (x² + y²) dx dy

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Q: Write a polar equation of the formr cos(0 – 0) = ro for the line x - V3y = 2.

A: We have to solve given problem: