Q2/ Calculate f F.dr, where (x2 + y?)i - (2xy)j + xk , if the contour is that portion of the circle x²+y-a' from the point (a,0,3) to the point (-a,0,3). (-a.0,3) (a.0,3)

Q: A circle has its center at (3,-2) is tangent to the line 3x+4y-26=0. Compute the point of tangency…

A:

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

A:

Q: he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

A:

Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

A:

Q: Q2 Calculate 8- z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Sketch the section of the surface at x = 0. y? - 25z? = 25 12 -12 -8 12 -4 -8 -12 4 -6 -2 -4 4.

A: topic - hyperbola

Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: Q2 Calculate 8- z dz, z(4- z) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: Evaluate (x+ y)ds where C is the straight-line segment x = 3t, y = (12 - 3t), z = 0 from (0,12,0) to…

A: We need to evaluate the integral along the given line. First eliminate the parameter t.

Q: 35. In the xy-plane, the circles with equations (x-3)² +y² = 11. and (x+2)² + y² = r² |3D %3D 2re…

A:

Q: Sketch a contour diagram for f(x, y) = x2 − 2y2 with three labeledcontours.

A: To sketch the contour diagrams for the given function of two variables

Q: Find the center of the circle tangent to x^2 + y^2 + 2x - 6y + 5 = 0 at (1,2) passing through the…

A: First find the equation of the tangent. The point (1,2) is tangent to the given circle. The general…

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: Q2 Calculate 8-z dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: b) Find the shaded area of diagram that shecked by curve y =x² + 2x and the line y

A: The area between curves y=f(x) and y=g(x) on an interval [a, b] where f(x)≥g(x) on the interval is…

Q: Determine parainetric cquations for the line L representing the interscction of the planes x – y +…

A: Given equation of plane are:-           x - y + 2z = 0 and             3x + y - z = 1

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

A:

Q: Q5. Prove that the circle {(x, y), x² + y² = 1} is not homeomorphic to the interval [-1, 1].

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

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

A:

Q: Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4)…

A: The given integral is: ∫C -ydx+xdy Where C consists the curve along the horizontal line from -4,4 to…

Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x2 +…

A: According to the given information it is required to calculate both sides of the Green’s theorem.…

Q: Q2 Calculate 8-る dz, where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

A:

Q: C is the part of the circle of radius 3 in the first quadrant from (3,0) to (0,3) and F = (1, -y),…

A: Given, C is part of circle of radius 3 in the first quadrant from (3,0) to (0,3) and F=[1,-y] The…

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: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Q7// Find the distance between line L1:y=2 x+6 and circle with .center (1,2) and radius 2

A: The distance between the circle and the line is equal to the perpendicular distance between the…

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4) %3D 25 ix + O b. y = 7 O…

A:

Q: Find the length of the curve 3x = (y² + 2)³/2 from y = 2 to y = 3 %3D

A: Use length of curve formula:-  for a given curve x = f(y) from y=y1 to y=y2 length of curve,…

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

A:

Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

A:

Q: Evaluate f. y3 dx - x3 dy where c is the circle x2 + y2 = 4

A:

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A:

Q: Find the length of the curve. 3/2 y = (4 – x2/3 )2 %3D from x = 1 to x = 8 %3D %3D

A:

Q: Determine the equation of a plane parallel to x-z plane which is tangent to the circle…

A:

Q: Integrate counterclockwise dz, C' the circle with z² + 8z + 15 center -3 and radius 2. dz = La z2 +…

A:

Q: Find the maximum and minimum values f(1, y) = zy takes on the circle %3D r + y² = 12.

A: Lagrange multipliers method: First solve the following systems of equations: ∇fx,y=λ∇gx,y. The…

Q: Find the exact length of the curve. y = (1 + x*,3/2, OSxS 5

A: The curve is y=231+x232 , 0≤x≤5

Q: Sketch the surface given by the function. z= 9-x?-y? 2x -2 2x

A: Answer

Q: Find an equation of the tangent plane to the surface z = y? - x² at the point (-4,5,9).

A: Finding partial derivatives with respect to x and y for finding plane equation.

Q: Find an equation for the tangant line to the circle x2 +y² = 2 at the point (1,1 (hint: use the…

A: The slope of the tangent at any point on a curve is equal to the first derivative of the function at…

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

A:

Q: Q2 Calculate 8- Z -dz, (4 – 2) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: 23/ Find the angle between two curves: 3 y = 2 - x² , y = x²

A: The angle between two curves is given by the formula tan θ=f2'x0-f1'x01+f1'x0f2'x0 Given,…