4) Consider the images of the hyperbolas x² – y² = ±c² under the mapping f(z) = z², where c > 0. Show that you have two sheets on the image and show how these sheets are glued together so that f %3D becomes one-to-one and onto this new surface.

Q: 3. Using the traces obtained in IV.1., provide a hand-drawn sketch of 3. Label all important points…

A:

Q: Use the method of Lagrange multiplier to determine the maximum and minimum values of f(x, y) = x* +…

A: Local Maximum and Minimum by using lagranges Multiplayer.

Q: 7. Derive the orthogonal trajectories of the family of hyperbolas xy = c. %3D

A: The solution are next step

Q: 21 コミメ-2 of the with the Parabola y=z Find the hく line area region bet ween the

A: Let us consider the double integration I=∫D∫f(x,y) dxdy where  D=(x,y)|a<x<b,…

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

A:

Q: Find the asymptoles of the funchon given Hx)= x²- 5x+6 below X-2

A:

Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

A:

Q: Describe in words the level curves of the top half of the sphere x2 + y2 + z2 = 1.

A: Top half of the sphere will be a hemisphere.

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

A:

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

A:

Q: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

A:

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

A:

Q: Find the minimum of f(x,y) = 3x + 3y on the ellipsoid 3x2 + 3y = 2. Leave your answer correct to two…

A:

Q: The orthogonal trajectories to the family of hyperbolas xy= C is given by the family 1)y=cx 2)y2 -x2…

A: We need to find the orthogonal trajectory to the family of hyperbola xy=c

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

A:

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0).

A:

Q: Let C be the boundaries of the ellipse +=1 taken in the 9 16 counterclockwise direction. A…

A: We have to check

Q: b) If we are at the point (1, 2, 4) on the surface z = xy², and we move a short distance in the…

A: Please check step 2 for solution.!

Q: If PP' is a diameter of the rectangular hyperbola xy = c' show that the locus of the intersection of…

A: given , if PP' IS a diameter of the rectangle hyperbola xy = c^2  show that the locus of the…

Q: Use the method of Lagrange multiplier to find the largest and least values of h(x, y) = x2y on the…

A:

Q: Sketch the surfaces HYPERBOLOIDS (y2/4) - (x2/4) - z2 = 1

A: we have to sketch the surface of the hyperboloids  y24-x24-z2=1

Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

A:

Q: Find the points on the ellipse 2x +y = 1 where f(x,y) = xy has its extreme values.

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

A:

Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

A:

Q: Find the minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

A:

Q: Find an equation of the tangent line to the hyperbola defined by 5x^(2)+4xy−2y^(2)−4x=19 at the…

A:

Q: Obtain the Solution x, y > 0, xy > 1 of 1 the PDE Ury Such that x+y 2у и 3 0, их on the hyperbola…

A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

Q: . (a) Show that as (x, y)→ (0, 0) along any straight line y = mx, or along any parabola y = kx², the…

A: Given : f(x) = x³y/(2x^6+y²)  To find : To prove that limit exist along parabola

Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

A:

Q: The semi-hyperbola H(X)=(sqrt(x^2-1)) is continous at which x interval?

A:

Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

A:

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u                  (1) write down the subsidiary equation of (1)…

Q: Find the maximum and minimum valves of f(xy)=5x+Y on the ellipse X+36y=!

A:

Q: Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

A: We need to find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

Q: Find the asymptoles of the funchon given below Hx)= x²- 5x+6 (x-2) Cx+3)

A:

Q: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

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Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

Q: -8x If the infinite curve y = e8x, x 2 0, is rotated about the x-axis, find the area of the…

A: Given curve is y=e-8x, x≥0 is rotated about x axis.

Q: Find the points on the surface z²2=xy+1 that are closest to the origin using LaGrange multipliers

A:

Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

A:

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x²+ y²+ z²= e2x

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

Q: Find the points on the surface 2 2 xY + 100 that are closest to the origin.

A: