Q : Let: z, 1-i and z2 = V3+i. Find z, 22 in the polar forn

Q: 21. Let D be the parallelogram in Figure 13. Apply the Change of Variables Formula to the map G(u,…

A: Given first find out

Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: Find div F and curl F if F(r, y, z) = 10e i- 2 cos yj+ sin2 zk. %3D

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Q: Determine L{5 – 3t + 4sin2t – 6e"} by using the Laplace table

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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: Let D be the unit disk: x + y² < 1. Evaluate I| 7exp(x² + y²) dx dy by making a change of variables…

A: Given:The integral

Q: 9. It is recommended that you use polar Evaluate ffe (3x + 2y) dà where Ris the region in the upper…

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Q: Find the decomposition of a(t) a = arT + anN into tangential and normal components for r(t) =…

A: Given

Q: Evaluate eVf •dr where f(r,y, 2) = 4rye² and C is the path parameterized by r(t) = cos² t i +…

A: Given: fx,y,z=4xyezrt=cos2ti+sin2tj+tantk0≤t≤π4 Formulas used: ddxxn=nxn-1ddxex=exddxfgx=f'gx·g'x…

Q: Q. Let f(z)= u(xy)+ i V(x>Y) be analytic function and Z= re Find the Cauchy - Reimann eguations in…

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Q: Using the r, a, beR*parameters, we parameterize the y1 ,Y2: R° helices as follows. Y1:t → (r…

A: The parameterize the γ1,γ2 :ℝ3 helices are γ1:t→(r cos(at), r sin(at), abt)γ2:t→(r cos(-at), r…

Q: Let y be a positively-oriented parametrization of the simple, closed, four-point star connecting the…

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Q: Given, (2z – z) dz along the directed line segment from - i to 1. What is a parametric form of z(t)?…

A: We have to form a line segment from -i to 1 Let 0≤t≤1

Q: Let S (-7, 7) x Rx {0} and S2 = Image() where (u, v, 0) = (cosh v cos u, cosh v sin u, v). %3D…

A: Given: S1 = ( -π, π) * R *{0} S2 = Image (ϕ ) In which, ϕ (u,v,0) = ( cosh v cos u, cosh v sin u, v)…

Q: Let G(u, v) = (, uv). Use the Change of Variables Formula to compute the area of the image of [1, 4]…

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Q: Examplei Let M be on elliptic parobolbid x= y?4z? a) Find klu) at P= (4, to 12 2. b) Compute the…

A: Given equation of elliptic paraboloid is x=y2+z2              (i) Differentiating x w.r.t y and z…

Q: Suppose that u = Va2 – y? and v = arcsin() where x-y 0 and- . Which of the following is/are true? A.…

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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: du If u = x²y + y²z + z?x then at (1,1,0) is ax %3D -

A: Given that u=x2y+y2z+z2xTo find :∂u∂x  at 1,1,0Solution :u=x2y+y2z+z2x∂u∂x=2xy+0+z2∂u∂x=2xy+z2

Q: Let u = cos(r + y), x = 2st +t and y = t – 2s. Use the chain rule theorem to compute du for du and…

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Q: In AKLM, R is the centroid. If RQ=10 find LQ. L N P R K M

A: In ∆KLM The centroid of a triangle is "R". The length of the RQ=10. The objective is to find the…

Q: Find the first and second fundamental form of x(u,v)=(e(u-v)/2 cos(u+v)/2, e(u-v)/2…

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Q: If F(x, y, z) = –2i – 2æj – yk and G(x, y, z) = –2xi – yj – 2zk, find curl(F × G).

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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: find the decomposition of a(t) into tangential and normal components at the point indicated (1. 4r².…

A: Let r→t be a vector-valued function that denotes the position of an object as a function of time.…

Q: 3. Use the transformation u = 4, v = xy to find || ry³ dA over the region R R in the first quadrant…

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Q: 2. Obtain the eccentricity e and centroid a, and y. of the following image. f(x.y)=1 (object: dark)…

A: From the figure, we have to write down all the dark box function, for which f(x,y)=1 x,y=3,2, 4,2,…

Q: Let F = (tan-(3x) – y)ỉ + (-2x + sec¬1y)j and C be the boundaries of the circle x? + (y – 4)² = 9 in…

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Q: Consider the following. C: line segments from (0, 1) to (0, 4) and (0, 4) to (3, 3) (a) Find a…

A: Given: Path C is line from (0, 1) to (0, 4) and (0, 4) to (3, 3). a) C is a piecewise smooth curve,…

Q: By converting the integral 1-f dvdx into polar coordinates, the limits of integration of o are:…

A: The limit of x is from  -1 to 0. So, the theta can not be in the first and fourth quadrants. The…

Q: Let F = . [[ curlF d5 ,where Use Stokes' Theorem to evaluate S consists of the top and the four…

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Q: iven that use the bhi tzS to compute %3D irst shifting Theorem [e"e cos 7+]

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Q: Use the polar coordinates to evaluate volumes : 1) Below z = x2 + y² above z=0 , inside x² + y² = 9

A: As you not mentioned the question number and both question has independent solution  so according…

Q: Let F . // curlF d5, where Use Stokes' Theorem to evaluate S consists of the top and the four sides…

A: Given function is F=xyz,xy,x2yz Now calculate the curl F curl…

Q: Consider the following. C: line segment from (0, 0) to (4, 8) (a) Find a parametrization of the path…

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Q: Suppose F(x, y) = (3x – 4y)i + 2xj and C is the counter-clockwise oriented sector of a circle…

A: Suppose F(x,y) = (3x-4y)i + 2xj and C is the counter-clockwise oriented sector of a circle centered…

Q: Use Green's Theorem to evaluate x dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: 2. If o = x²yz³ and F(x,y,z) = 3yzi + x²j + (x cos y)k, find: a) grad o %3| b) div F c) curl F

A: Given:  φ=x2yz3F→x, y, z=3yzi→+x2j→+x cos yk→ To Find:  a grad φb div F→c curl F→

Q: Let F = -2yi + 2xj. Use the flux form of Green's Theorem to compute F·n ds where C is the positively…

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Q: B) Use Green's Theorem to evaluate F-dr, where C is the triangle with vertices (0, 0) (3,0) and (3,…

A: Explained below

Q: Let r(t)=⟨sin(t),cos(t),9sin(t)+3cos(2t)⟩. Find the projection of r(t)r(t) onto the xz-plane for…

A: Set y=0 as the answer is asked for xz plane.

Q: (b) Given  = (x²y)î + (xz – z²)f – (xyz)k, determine the following at point (1, 1, 2): (i) V- Â.…

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Q: The Jacobian J (r, Ø) for the transformation x =r cos(Ø) + 100000 y = r sin(Ø) + 500000000 at r= 2,…

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

A: Solution