17. Let f(x, y) xy. Find the minimum and maximum values on the ellipse x² + 4y² = 4.

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: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

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

A: The solution are next step

Q: Find the points on the ellipse 2x + 4y = 1 where f(x.y) = xy has its extreme values.

A:

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

A:

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

A:

Q: 1. Find the minimum distance from the point (0, 0, 0) to the plane x- y+z = 3.

A: perpendicular distance

Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

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

A:

Q: Find the points on the surface x2 - zy = 4 closest to the origin.

A:

Q: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: Q3 Find dyldx on the graph y secx + y = cos2x at point (1, 2).

A: We have to find the derivative of above function at (1,2) Please see the explanation below

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) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

A:

Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

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

A:

Q: Find the tangent line. To the ellipse x²+4y²=8 parallel to the line x+2y=6

A: Equation of ellipse is , x2+4y2=8Differentiate w.r.t.x2x+8ydydx=0Subtract 2x from both…

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

A:

Q: Let f(x, y)=sqrt(2x²+4y² +8) -x. The domain of c for which the level curve f(x, y) = c is an ellipse…

A:

Q: 4. Graph the surface 1 = y² + z² by first sketching at least three cross sections in each of the 4…

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem…

A:

Q: Find the points on the surface z2 = xy + 4 closest to the origin.

A:

Q: 8. Calculate fo F • dr, where F(x, y) = y² i + (6x + 6y)j, and C is the portion of the parabola 2y²…

A: Given curve is 2y2-x=1 and points are (1,-1) to (7,2)

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

A:

Q: Find a generating curve and the axis of revolution for the surface                             x2 +…

A: Find a generating curve and the axis of revolution for the surface   x2+3y2+z2 =9 If the equation of…

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

A:

Q: Use Lagrange multipliers to Önd the points on the ellipse 2x2+y2 = 1 where f (x, y) = xy has its…

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: Find an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 +…

A: It is required to find the equation of generating curve given the equation of its surface of…

Q: Find the maximum and minimum values of f(x, y, z) = x - z on the ellipsoid x² + 2y? + 22 = 1.

A: maximum=? minimum=?

Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

A:

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: Find the minimum of f(x,y) = 4x + 5y on the ellipsoid 9x2 + ly2 = 7. Leave your answer correct to…

A:

Q: Find the extreme value of the function f(x, y) = xyon the ellipse x2 + 2y2 = 1.

A:

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

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: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

A:

Q: Find the points on the curve of intersection of the ellipsoid x² + 4y² + 4z² = 4 and the plane x –…

A:

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

A:

Q: Find the absolute maximum and absolute minimum of the function f (x, y, z) = x³ + 2y along the curve…

A:

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

A: Topic = Geometry

Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

A:

Q: Let f(x, y) = x? + 4y. Find the extreme values of f on the ellipse x? + 2y? = 1.

A:

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 c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

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: Let f(x, y) =V2x²+4y2 +32 -x. The domain of c for which the level curve f(x, y)=c is an ellipse is

A: For the solution follow the next step.

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

A: