4. Evaluate 3x?ev° dx + 2x°ye° dy where the open curve C is the semicircle x² + y² direction. 5, y > 0 going in counterclockwise

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Q: 2.) Find the acute angle between the given curves y² = 2x and 4x²+ 4y² +5y=0

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Q: 6 Consider points P and Q in the x-y plane, with P = (1,0) and Q (0,1). The line integral %3D %3D Q…

A: Introduction :Given, two points P and Q .P= (1,0)Q= (0,1)We have asked for the line integral of

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Q: 3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented…

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

Q: 4. Where does the curve r(t) = ti + t²j+ (3 t2)k intersect the paraboloid z = x2 +y² ?

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Q: D A Find thepolar eavation for the cartesian curve (x²ty) - A)r-4 cos o =4x. Br°=4 cos e c)r?=4cos o…

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Q: sketch the solid whose spherical coordi- nates (p, 4, 0) satisfy the given inequalities. 0<p<2/cos…

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Q: At what points does the curve  r(t) = ti + (5t − t2)k  intersect the paraboloid  z = x2 + y2

A: We have to find the intersection point

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Q: Evaluate [. 2y² + 4z² ds, where o is the first octant portion of a cone z = x² + y2 with height of…

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Q: 7. Given that the line y = r -b is an asymptote to the ar curve y a,b €R,rz 1, then b = A -1-a 1-a C…

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Q: 19. Evaluate Scx ds, where C is a. the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).…

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Q: 1)calculate a*yz dædydz where D is the rectangular parallelepiped 1< « < 2,1 < y < 2,1 < z < 5

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Q: At which of the points below is the tangent plane to the surface - 2y² + z²+ yz = 2 vertical? Select…

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Q: Calculate a 3 ydz t 13x'y dy, Where Cis the oriented curve given in the figure . 3 Bydr+43xy dy =?…

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Q: 10. If ZYXW is an isosceles trapezoid with WY = 15x-2 and XZ = 9x + 10, find x. X 1 partn Z Y

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Calculate | [(a* – 3y) dæ + (2y³ + 4x) dy] wherein y(t) = (3cos(t), 3sin(t)), 0 <t < 2ñ, is an…

A: Please check step 2 for the solution.!

Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

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: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

Q: Use the Green's theorem to calulate So (3x²y – xy? – 3.x²y²) dx + (x³ – 2.x³y+ x²y) dy, where C is…

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Q: 8/ find the product of integretioh 2 (4X+17XY+4y?)dA We rhow thort Dis Hhe delihited Yegion, but…

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Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

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Q: If the infinite curve  y = e−8x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A: Given: y=e-8x , x≥0

Q: 8/ find the Product of integratioh (4X'+17XY+4y?)dA We rnow thort D is the delihited Yegion, but…

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Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

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Q: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-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: Jse Green's theorem to evaluate $ (2°e* + 4y) dz + (-5x+ y* sin(y)) dy, where C is the…

A: The given path C is circle x2+y2=16. Therefore: D= (x, y) : x2+y2≤16

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: find the Jolume of the salid genereted by revaling- the curve 4t'qy=36 between y = 0. and g=2 Gbout…

A: The objective is to find the volume of the solid about y-axis.

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: Line integrals

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

A: The green's theorem states that "line integral over a closed curve C…

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x² + y2? (If an…

A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x2 + y2? (If an…

A: knlk

Q: Are there any points on the hyperboloid r² – y² – 2² =1 where the tangent plane is parallel to the…

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Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

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Q: If the two spheres (x-4)^2+(y-1)^2+z^2=27 and (x-13)^2+(y-10)^2+(z+9)^2=a are externally tangent to…

A: Consider the given two spheres x-42+y-12+z2=27 and x-132+y-102+z+92=a are externally tangent to each…

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