Let ƒ(x,y) = x²e"9. Give the unit vector that points in the direction of maximum increase along the surface when (x, y) = (1,1).

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Q: Determine the flow rate of water across the net if the velocity vector field for the river is given…

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Q: Find a vector-valued function whose graph is the indicated surface.

A: Given : The plane x + y + z = 6.   To find a vector-valued function.

Q: A point moves along the intersection of the elliptic paraboloid z = x² + 3y² and the plane y = 1. At…

A: Point moves along the intersection of the elliptic paraboloid z=x2+3y2 and the plane y = 1. We have…

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

Q: Let f(x, y) = x²y'. At the point (-1, 2), find a vector (a) In the direction of maximum rate of…

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Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: Sketch the space curve represented by the intersection of the surfaces           x2 + y2 + z2 = 16,…

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Q: A normal vector to the tangent plane for the at the point (1, 1, 1) is: y surface x =

A: A(1, 1, 1)z= xyf(x,y,z) =xy-zfx=yfy=xfz=-1Normal vector to the tangent plane for the surface;n^…

Q: Let F(x, y, z) =7x2+8y2+13z2. Find the equation to the tangent plane to the level of surface F(x,…

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Q: The vector (x, 2y, –3z) is normal to the surface x2 + 2y? – 32 – 4 = 0 at any point (x, y, z). - - -

A: Let's find.

Q: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at…

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Q: Find the directional derivative of f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: To find the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point (1,3)…

Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: Compute the vector line integral: x – 4 dx + (x – 4)² + y² -y dy :- 4)2 + y² where C is the circle…

A: To find the below vector integral. ∮C−yx−42+y2dx+x−4x−42+y2dy

Q: A point moves along the intersection of the elliptic paraboloid z = 3x² + 5y² and the plane y = 4.…

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Q: Find the directional derivative of the scalar function of (x, y, z) = xyz in the direction of the…

A: Given surface is z=xy

Q: Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate…

A: As the given plane tangent to z=f(x,y) at (-2,3,4) is  4x+2y+z=2, that is z=2-4x-2y thus the…

Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: Find the direction in which the maximum rate of change occurs for the functio f(r, y) = 2x sin(ry)…

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Q: Find the equation of the tangent plane to the surface z = In (2x + y) at the point (-1, 3, 0) . O x…

A: The equation of the tangent plane to the surface Z=fx,y atthe point a,b,fa,b is given by…

Q: Find equations of the normal line and the tangent plane to the parametric surface defined by the…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  compare coordinate on…

Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 7y and the planex = 1. At…

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Q: Let f(x,y)= e, Compute the cartesian equation of the tangent plane r,y) at the point (2.2).

A: The equation of tangent plane

Q: Find the directional derivative of the scalar function of (x, y, z) = xyz in the direction of the…

A: What is Gradient of a Scalar Function: The gradient of a scalar function is vector quantity. It is…

Q: Find the point (x, y, z) on the surface z = 2x2 - y where the tangent plane is parallel to the plane…

A: We have to find the point (x, y, z) on the surface z = 2x^2 - y^2 where the tangent plane is…

Q: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

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Q: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of…

A: Equation of a line passing through point (a, b, c) and parallel to vector <p, q, r> can be…

Q: Find a unit vector n that is normal to the surface 4z? – 2x* – y = 18 at P = (1,2,3) that points in…

A: Solution of question is written in below steps.

Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 4y and the plane y = 4. At…

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Q: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

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Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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Q: Find rectifying plane of et, é, t at the curve t%3DL

A: Given curve is αt=et,e-t,2t.  To find the rectifying plane of the curve . Result: Let rt→=xt,yt,zt…

Q: 1. Let f(r, y) = arctan(ry). (a) Find the unit vector in the direction where the directional…

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Q: Find a nonzero vector normal to the plane z − 5(x − 1) = −2(3 — y). - -

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Q: The level curves of the surface z = x2 + y2 are circles in the xy-plane centered at the origin.…

A: Consider , Equation of the surface given:  z = x2 + y2 The level plot is as shown below:

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: Compute the directional derivative and gradient of f(x, y, z) = 4r – yez at (2, -1,0) in the…

A: Given: fx,y,z=4x-y2e3xz       at     2,-1,0 Directional Derivative = Gradient of function x unit…

Q: What is the equation of the tangent plane normal to x2 + y2 + z = 9 at the point (1, 2, 4)? O 2x -…

A: Given; f(x,y,z)=x^2+y^2+z-9  Point (1,2,4)

Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: Find the a unit vector in the direction of which f(x, y) = In (1 + xy) increases the most rapidly at…

A: Consider the given function as fx,y=ln1+xy

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

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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 a vector function that parameterizes the curve of intersection between the surfaces y^2-z^2=x-2…

A: To determine the vector function for the curve of intersection between the surfaces.

Q: Suppose n is a vector normal to the tangent plane of the surface F(x, y, z) = 0 at a point. How is n…

A: We have asked how a vector n which is normal to the tangent plane of the surface F(x,y,z)=0 at a…