Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x-2)²+(y-3)² = 4 Without using Green's Theorem.

Q: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: 6. Determine the equation of the circle whose center is at (4, 5) and tangent to the circle whose…

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

Q: use green's theorem to evaluate ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4 counterclockwise

A: Given: ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4

Q: 2. Evaluate dy, where C is the part of the parabola y = x² from (1, 1) to (2, 4).

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Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: z dz 2z ² +(1+i )z -i C is the circle |=|=2

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Q: Verify Green's Theorem where F1=y^2-7y , F2=2xy+2x and the curve C is a circle x^2+y^2=1

A: Given: F1=y2-7y , F2=2xy+2x and C is a circle i.e., x2+y2=1 As, we have:…

Q: Use Green's Theorem to find (8y + x) dx + (y + 2x) dy, where C: The circle (x - 4)2 + (y-3)2 9 541…

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Q: 2: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x–2)²+(y-3)² = 4 | a) Using Green's Theorem

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Q: Sketch the graph of y = m(r) in Figure 2. %3D 음-3, rS-1 m(x) = 4 %3D 1<r<5

A: Given,          mx=13x-3x≤-141&lt;x&lt;5

Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: 6. Let C C R? be the positively-oriented boundary of the graph of the circle x2 + y? = 1. Using…

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Q: =2) Calculate & ydx + xz² dy - zy³ dz, where c is the circle x² + y² = 4, Z=3 (conterclockwise)…

A: We will use stokes theorem to find integral

Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: A surface in R³ is defined by the equation 4z = x² + 4y².

A: Given:-                 The surface in  is given by  . Sketch the intersections (traces) of this…

Q: 16 6xy ds, where C is the right half of the circle x² + y² = 4. Evaluate the line integral

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Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

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Q: (2) Find the Ualue of the constant m while the Curl of Foaoy,z) = (mxy- 2) Ĉ +cm-2)x)+(1-m)x2° Â is…

A: Please see the answer in step 2

Q: 4. Evaluate y ds where C is the upper half of circle x² + y² = 9, traversed in the counterclockwise…

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Q: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

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Q: 4. Evaluate √3x²e¹² da + 2x¹yev dy where the open curve C is the semicircle x² + y² = 5, y ≥ 0 going…

A: 4. The given integral is ∫C 3x2ey2dx +2x3yey2dy where C is the semicircle x2+y2=5, y≥0 To find: the…

Q: 2. Use Green's Theorem to evaluate (7z +y) dy - (r² – 2y) dz where C is are the two circles as shown…

A: theorem:

Q: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: 4. Let C be the the circle ² + y² = 4 and Calculate the work(W = [,F dr when C is traversed in the…

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Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

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Q: i) Use the residue theorem to evaluate 2z+6 dz, where c is the circle |z – i| = 2. z²+4

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Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

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Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: D is the region enclosed by the parabolas z = y²-9 and 2 - y² +9.

A: Let, I=∫∫Dx+y+2dA x=y2-9 and x=-y2+9 Power rule for the integration: ∫xndx=xn+1n+1+C ∫cdx=c∫x0dx=cx

Q: Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4,…

A: The answer is as follows:

Q: dz b) C: z|= 4 is a circle calculate the integral .(z-1)(z² +9)

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Q: Express you answer in Mdx + Ndy = 0. 1. Circles whose center is passing through y = 4x %3D

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Q: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

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Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: Evaluate |(y zi+y°i+xzk)•d$ where S is the boundary of a cuboid defined by S -15x<1, -1<ys1 and…

A: The given integral: S=∬s(y2zi→+y3j→+xzk→) dS Where S is the boundary of cuboid defined by -1≤x≤1,…

Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: Find the equation of the integral surface of the PDE 2y(z- 3)p+(2x- z)q = y(2x – 3) which contains…

A: Here to finding the equation of integral surface to given partial differential equation we use the…

Q: Find the point on the curve of intersection of the paraboloid x – y + 2z = 0 that is dosest to the…

A: Here we have to find the point of intersection of the paraboloid x2+y2+2z=4 and the plane x - y + 2z…

Q: (a) Prove that the line 2x 3y + 26 =0 is a tangent to the curve x + y2 - 4x + 6y – 104 = 0 hence…

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Q: Q4: Evaluate fo z² - 3z + 1 z + 2i -dz 312 where C is the circle |z + 11 = ²/

A: