Find the work done by the Öeld F = yzi + (xz + 3)j + xyk along the line joining the point A(1, 2, 0) to B(2, 0, 3)

Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: 2. The function f(x,y,z) = xyz has gradient Vf(x,y, z) = (yz, cz, ry). Let C be the path from (1, 1,…

A:

Q: Bounded by the curve y = (x + 3)², the x axis, and the lines x =-3 and x= 0. %3D

A:

Q: Find the gradient of the function f(x, y, z) = xeyz, and the maximum value of the directional…

A:

Q: Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0)  and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

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: .    Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to…

A:

Q: sketch the graph xyz plane x^2+z^2=4

A: GIVEN: x2 + z2 = 4

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

A:

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: The points P= (x, x, x) and Q (y,3y.y-1) are lines in R' that do not meet. Choose x, y to %3D…

A: Given that P=x,x,x  and Q=y,3y,y-1 Then    P-Q=x,x,x-y,3y,y-1⇒P-Q=x-y,x-3y,x-y+1 then, we solving…

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

A:

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Maximize and minimize the function f (x, y) = 1+ 4x + 2y – 2x2 – y? on the triangle bounded by the…

A: We will find out the required value.

Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

A:

Q: The gradient vector of the function f(x, y, z) = ln(yz) - x² is: Select one: ○ (−2x,, 1) O None of…

A: To find the gradient vector of the functionf(x, y, z) = ln(yx)-x2

Q: Consider the function f(x, y) = 3x³ + 3xy² - 18x - y² Compute the stationary points of the function…

A:

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

A:

Q: Compute F · dr where F(x, y) = and C is the path traced by the line segment starting at (0, −1) and…

A:

Q: Find the linearization of y=√x  at a=49. Then use your linearization to approximate √56. Show work

A:

Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

A:

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: In the question it is asked to find the path of a heat-seeking particle placed at point P. Given:…

Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: (2x, /, // ) (2x, -, -…

A: gradf =∇f =i∂∂x+j∂∂y+k∂∂zf .

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A:

Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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 work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to (-1, 0,…

A: The gradient of f(x, y, z) is:

Q: Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+…

A:

Q: Compute the gradient of the function at the given point. f (x, y, z) = In(x² + 7y – 3z²) ; (7,7,7) O…

A:

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: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 0, 1)  and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: Find the absolute maximum and minimum of the function f(x,y) = 2x² - 4x + y² - 4y +6 on the closed…

A: Given that a function f( x , y ) =2x2-4x+y2-4y+6  on the closed triangular plate bounded by the…

Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

A:

Q: Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y)…

A:

Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: : Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A:

Q: speed of a particle with position function r(t)=⟨8cost,−6t,8sint⟩r(t)=⟨8cos⁡t,−6t,8sin⁡t⟩ ⟨v(t)=⟨ ,…

A:

Q: Region Ris enclosed by the curve y = 2 Vx – 3, the line y = 4, and the line a = 3. y = 2/z – 3 y = 4…

A:

Q: Find the extreme values of the function f (x,y) = 2 - 4x - - y² on the closed region bounded by the…

A:

Q: Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: determine the gradient and equationof the tangent to the curver f(x,y) = 0 in the point (a,b) for…

A:

Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: The gradient vector of the function f(x, y, z)= ln(yz) - x² is: 2 Select one: 0 (-2x,1,1) O None of…

A:

Q: Find the linearization of f(x,y) at the indicated point (X0:Yo). f(x,y) = In (x +y); (6, 1) L(x,y) =

A:

Q: Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

A:

Q: Find the work done by the gradient of ƒ(x, y) = (x + y)2 counterclockwise around the circle x2 + y2…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.