Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5 , 0) and (0, 1).

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

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

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Q: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

Q: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

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Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

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Q: Find the uolume of the soild olbtained by the grophs bounded by potaling the begion Y = x² +1 and Y…

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Q: Find the orthogonal trajectories of the famil y of curves x'yxy=c where cis constant

A: Given:    x3y-xy3=c      Differentiating by using power rule we get…

Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

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Q: Obtain the orthogonal trajectories of xy = C and compute for the positive value of y at the point…

A: Solution

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: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

A: The standard form of the equation of the hyperbola is,

Q: he upward flux of

A: Introduction: Let F be a function and let the region is S, then the flux of the function is given…

Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

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Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Find the orthogonal trajectories for the families of curves y+x^2 = w where w is a parameter

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Q: Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: Find the absolute minimum and absolute maximum of f(x, y) = 10 – 2x + 3y osed triangular region with…

A: Given: f(x, y)=10-2x+3yWith vertices (0, 0), (3, 0) and (3, 4)

Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: Find the absolute minimum and absolute maximum of f(x,y)=19−9x+13y on the closed triangular region…

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Q: Find the positively oriented simple closed curve C for which the value of the line integral     (y3…

A: The line integral is  ∫C(y3 − y) dx − 9x3dy The expression for Green's theorem is  ∫CP(x,y) dx…

Q: Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 + y2 + z2 < 1.…

A: fx,y,z=2xyz on the unit ball x2+y2+z2≤1 gx,y,z=x2+y2+z2-1 ∇f=∂f∂x,∂f∂y,∂f∂z ∇g=2yz,2xz,2yx…

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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Q: Find the maximum and minimum values attained by f(x,y,z) = xyz on the unit ball x2+y2+z2 ≤ 1

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Q: find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the…

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Q: 2 Find the points on the curve ax+ 2bxy + ay = c,ay = c, 0<a<b<c,whose distance from the origin is…

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Q: Find the absolute maximum and minimum values of the function on the triangular region whose vertices…

A: The given function f(x, y) is a polynomial and therefore, it is continuous and has both maximum and…

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

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Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. f(x,y) = x4 - 4xy +…

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Q: Find the lineanzation LlXiy) of f (iy) =x*-5Xy at (2,1). Then use the linearization to approximate f…

A: Here in this question we need to linearize the given function and then approximate the value of…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: The curve y = (64x – 4x³ )m bounds the shaded section on top and the x-axis on the bottom. Determine…

A: Given curve, y=64x-4x3 The shaded region is shown as: Formula for the centroid x, y in a region is…

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: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…

Q: Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular…

A: Given:- The function is, f(x,y)=3xy-3x-6y+1on the closed triangular region whose vertices are (0,0),…

Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

Q: Find the direction of maximum change of f(x, y, z) = xey + z² at (1, In 2,2).

A: Introduction: A function's maximum directional derivatives at a particular point P are produced in…

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

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Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…

A: Given: The equation of ellipsoid is 3x2+y2+3z2=1 and the equation of the plane is -12x+2y+6z=0.…

Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

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