If the analytical function f(z) = u(x, y) + iv(x, y) is expressed in terms of the polar coordinates r and 0, show that 1 dv and 1 du du %3D ar r ae or r de

Q: Change the Cartesian integral into an equivalent polar integral. 2 2 a -x 00 S SO dy dx = dr de 2 2…

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Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a =…

A: Consider given expression is, y=asin(bx2) Then, y=12sin(4x2) The given value of x=0 and x=πb that is…

Q: x y 11. Use Green's theorem to evaluate O In(1+ y) dx –- dy , where C is the triangle with vertices…

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Q: Evaluate the spherical coordinate integral. 1- cos 2 2x x SS S p²sin dp do de 00 1- cos 2 2x x SS S…

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Q: The speciat sotution to the equatio %3D ho A/y)=+X B/yo)=y - %3D d/other than that

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Q: Convert the integral V10 dy dx polar coordinates and evaluate it (use t for 0): With a = ,b = c =…

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Q: Q.1) Use the polar integral to evaluate /1-(r-1)² r+y dydr 1² + y?

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Q: 2: Use the polar coordinate to find the integral (x+y') dxdy 0 0 1/16 1/2 By using the change of…

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Q: 3. Evalnate. the. following.double.intagrals.by.comverting to Polar.Caa.r.dinates. 2 2 Anse. T(e-1)…

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Q: Q1) Evaluate the integral S S dy dx using polar coordinate

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Q: tIND THE AZEA OF THE RECION BOUNDED BY ムラ日ラ0 AND THE THE POLAR X-AXIS AY

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Q: 18. Show that the centroid of the sector in Figure 13 has y-coordinate 2R sin o (0, y) R FIGURE 13

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Q: Let u(x,y) satisfy the following equation uxx+(x2+y2-1)uyy=0 Find the region in which the equation…

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Q: 3 Evaluate the integral cos(x² + y²)dydx by converting to polar coordinates 0 0

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Q: Evaluate f (x + 2y)dx + (y – 2x)dy around the ellipse C defined by x = 4 cos 0, y = %3D | C 3 sin…

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Q: find the decomposition of a(t) into tangential and normal components at the point indicated, as in…

A: Consider the given information rt=eti+1-tj ,  t=0   Find the first derivative of rt…

Q: Find the linearization L(x,y) of the function f(x,y) = e 3× cos (9y) at the points (0,0) and 0,

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Q: find the decomposition of a(t) into tangential and normal components at the point indicated r(t) =…

A: The given vector  rt=t,cost,sint ,      t=π2 To finding the components of acceleration take the…

Q: Let w = f(x, y) and x, y in polar cordainate then (fr)² + (fy)² =

A: We are given that w=f(x,y)            ........(1) x, y are in polar coordinates. So, in polar…

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &3, x2-y2=3 &4 Where u=xy and v=x2-y2

Q: Q1) Evaluate the integral N 4-y2 dx dy using polar coordinate

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Q: find the decomposition of a(t) into tangential and normal components at the point indicated, as in…

A: Given: r(t)=(t,cost,sint)t=π2

Q: Evaluate the line integral (cos x + sin y) ds; C is the line segment from (0, 0) to (x, 67).

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Q: Consider the curve described by the parametric equations x = t° +1, y= t² – º. Compute the area…

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Q: Consider the transformation x = p sin ø cos 0, y = p sin ø sin 0, z = p cos o from spherical to…

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Q: Sketch the D indicated and integrate f(x, y) over D using polar coordinates. f(x, y) = 16xy; x > 0,…

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Q: In changing the differentiating variable to a polar coordinate system, A. dx and dy becomes dr and…

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

Q: y = sec t, x = cosec t %3D %3D

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Q: b) Use the polar coordinate to find the integral S+y) dxdy

A: See the attachment

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x – y)dy for the given path. C: x =…

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Q: Find the equation for the Tangent Plane on the given surface coS ax – x²y + e*z+ yz = 4 Po(0, 1, 2)

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Q: 39. Show that the graph of r =t sin ti + t cos tj + t'k lies on the paraboloid z = x² + y².

A: Here we compare r as its basic equation to prove this.

Q: 7. To convert the following cartesian integral to polar, the double integral becomes, * cos (x² +…

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Q: Let r(t) = (sin(t), cos(t), 5 sin(t) + 4 cos(2t)). Find the projection of r(t) onto the xz-plane for…

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Q: Question 9. Let N = {1< x² + y² < 4, x < 0} be a domain in R². Use Green's Theorem to evaluate…

A: We have to evaluate the integral ∫x2y2dx+x3ydy using the Green's theorem over the region…

Q: Suppose that the polar coordinates of a moving particle at time t are (r(t), 0(t)). Prove that the…

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Q: Use polar coordinates to evaluate the double integral V1 1-z2 dy dæ. (1+z² + y?)²

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Q: Use Green's Theorem to evaluate | (v? – tan-1 x²)dx + (3xy + 4x – In (y2 + 4))dy where C is the…

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Q: Use polar coordinates to evaluate the double integral 2 1 – a²- dy dx. (1+æ? + y²)²

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Q: Given: f(x,y)=x-2y+3 and D is inside x +y =16 and to the right of the y-axis. Write the integral K =…

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Q: 1) Use Green's theorem to evaluate o y'dx-x°dy where C is the curve shown: r2 where ri=3 and r2=5…

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Q: 1. Evaluate the integral: VI-x² (b) e-a²-y° dy dx (Hint: Use polar coordinates)

A: Given:

Q: Q1: convert the Integral So √1-x² (x² + y²)dydx to the polar coordinates. 277

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Q: Consider the transformation x = p sin o cos 0, y= p sin o sin 0, z = p cos o from spherical to…

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Q: Q2: a) Use the polar coordinate to find the integral (x+y') dxdy ! -y 1/16 1/2 b) By using the…

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Q: 2. Convert the following double integral to polar coordinates and evaluate. S so dx dy 4y-y² Jx²+y²…

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Q: 3. Solve the Laplace equation inside a 60° wedge of radius 1 subjected to the boundary conditions…

A: The Laplace equation is given by: r2∂2u∂r2+r∂u∂r+∂2u∂θ2=0 The boundary conditions are: ∂u∂θr,0=0,…

Q: Show that the graph of ř = (t sin t, t cos t, t²) lies on the paraboloid z = x? + y?.

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = tan-1 (xyz) at…

A: Consider a function: fx, y, z=tan-1xyz……1   Given point, say A, is: A=1, 1, 1   On comparing A with…

Q: Find..aW and. au at. the. paint.(u.,.v.).(-2D). i.W.In (x+yz)X=u.e.sinu. y=uě.cosu.. and..z=u.e.

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