10. Derive CRE in polar coordinates Ur = r-1v0 ug = -rvr Using x = r cos 0 and y = r sin 0 and chain rule ди дх дх дү ди Ər ди дө ὃν ər ὃν дө = || = ди дх дх дө + dvdx дх дө + ди ду ду дә dvdx до ду -+ дх дr ' ду дr дә + диду ду дө до ду ду дө

Q: The relationship between rectangular coordinates (x, y) and polar coordinates [r, 0] can be…

A: According to question,Given equations,x = r cos θ,y = r sin θ,r = x2 + y2tan θ = yx

Q: 24/ Replace the polar equation r. sin (0 +") = 2 to Cartesian equation -(G+ ns./ = 2

A: The given polar equation is r·sinθ+π6=2 .................(1)

Q: Consider the following. u = (2, 0), v = (5, 7) (a) Find u · v. U'V = (b) Find the angle between u…

A: Given that  The vectors  u=(2,0) and v=(5,7) To find the u.v and angle between the u and v

Q: (a) Express j'(1- j) in polar form, leaving your answer in surd form. 7. (a) Solve the equation 2x?…

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Q: The polar equation r = a+a cos 8, where a > 0, has a tangent line at (0, 7)

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Q: 2. Use polar coordinates to evaluate 3 √9-x² -3 0 sin(x² + y²) dydx

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Q: 3. Find the linearization L(r, y, z) of the function f(x, y, z) = y² sin(2rz) at Po = (7,2, 4). Then…

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Q: #2) Convert each of rectangular pair coordinates to polar coordinates where r> o and o 4o < Zx. part…

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Q: Convert the rectangular coordinates (V8, v8) to polar form (4, ) a. O b. (2, ) (4. ) O C. O d. (v2,…

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Q: Convert the point (3, V5) from rectangular to polar coordinates with 0 < 0 s a/2. (Round your…

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Q: Convert to polar coordinates where r>0 and 0 <0 < 2n . (0, 3) OLATEX:…

A: The given coordinate point is (0,3)

Q: 2) Use polar coordinate dydx (1+ x² + y° )'?

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Q: Find the polar equation for the Cartesian curve x² = Or= Or T = Or= Ora 1 Or= -tan 0 2 1 2 1 sin 0…

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Q: 2. Give 3 other representation of the polar coordinate (changing the sign of r at least once). (2)

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Q: Q5/ Change the polar equation 2r = 2 + cos 0.(2r-1) to Cartesian equation Ans./y²-3x² - 4x-1=0

A: To find- Change the polar equation 2r = 2 + cosθ·2r - 1 to Cartesian equation.

Q: he polar equation for circle x^2+(y- 3)^2 =9

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Q: The gradient vector field for a function f:R2→Rf:R2→R is given in the attached image: f has a…

A: The graph for the direction field is given.

Q: 8. The point ( 5, can also be represented by which of the following polar coordinates? » (s -) s-똥)…

A: Given, Polar Coordinates 5,π6

Q: Sketch with directio

A: Given:  Three polar coordinates. We have to sketch the graph with their directions.

Q: 2. Convert the rectangle coordinate (1,-√3) to a polar coordinate (r, 0) with r>0,-2л ≤0<2.

A: Given query is to convert rectangular to polar coordinates.

Q: Q1// Converting r= 12 cos 0 r = 12 cos 0 from polar to the equation of a circle?

A: Given problem:- Converting r = 12cos(θ) from polar to the equation of a circle?

Q: l+vI+r² xy dydx -z 1-VT-

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