Find the maximum and minimum values of the function f (x,y) = 2x² – y² on the ellipse p² + 2 (y – 1)? = 2.

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

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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: At what points does the curve r(t) = t i + (6t - t2)k intersect the paraboloid z = x2 + y2? (Enter…

A: Given: Equation of curve:                                    r(t)=t i +(6t-t2) k Equation of…

Q: Determine the points on the surface y2+z2−x=8 that are closer to the origin.

A: Consider the given surface. y2+z2−x=8z2=8−y2+xf(x,y)=8−y2+x

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

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Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

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

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Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

Q: Use the method of Lagrange multipliers to find the minimum and maximum values of the function f (x,…

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

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

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: At what time t does the speed of a particle moving in 3-space with position function r(t) = ti+tj+…

A: To find the time at which the speed of the partial is minimum. Note that, the velocity is the time…

Q: 1- Find the minimum and maximum values of the function f(x,y) = 2x2 + 3xy + 2y2 + x - y inside and…

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Q: A heat-seeking particle is located at the point P(6,4) on a metal plate with temperature at (x, y)…

A: Given, a heat seeking particle is located at the point P(6, 4). The temperature function is given…

Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

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: Find a cubic function d cx bx ax x f + + + = 2 3 ) ( whose graph has a relative minimum at (0, 1)…

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Q: Write the general solution of the fourth-order DE y(4) – 2y" + y = 0 entirely in terms of hyperbolic…

A: We have to find the general solution of the differential equation y4-2y''+y=0. The auxiliary…

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…

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

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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 greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1…

A: Let's find.

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

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Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

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: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

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: 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 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 lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

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

A: Given

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

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Q: Q4/Find the abs.max and abs.min valuse of the huctu f,y) = \+xy-3x on the cosol regen oounded by the…

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

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Q: What do you mean by asymptotically stable for autonomous equations ?

A: Given: asymptotically stale for autonomous equation A critical point x∘ of an autonomous system is…

Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

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

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

A: This question is related to Lagrange multipliers theorem. We will solve this question by using…

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

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

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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: 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

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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: 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: 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

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.