Find ∫F • dR from (1, 0, 0) to (1, 0, 4), if F = xi - yj + zk along the line segment joining (1, 0, 0) to (1, 0, 4).

Q: Let y = 2x + 2x +3. If Ar = 0.2 at a = 2, use linear approximation to estimate Ay %3D Ay Submit…

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Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: Evaluate F. dr where F(x, Y, z) = (1.25yz cos(xyz), 1.25xz cos(xyz), 1.25xy cos(xyz)) 1 1 and C is…

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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: 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: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: Evaluate F dr, where C goes along the curve {x* + y* = 1, z = 2} from (1,0, 2) to (b) (0, 1, 2).

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Q: Let F(x, y) =x2+xyz+z , find at the point (1,1,1)

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Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: Find a linearization L(x, y, z) of f(x, y, z) = x²y + 4z at (1,-1,2).

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Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

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Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

A: As per Bartleby guidelines I have authority to answer only one question. If you want other…

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) =…

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

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Q: Compute f, f for f(z) = sin(5z) and path y that is the line segment from 3 – 6i to -6+ 6i.

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (4, 3)…

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Q: The gradient vector of the function f(x, y) = cos(4x - 6y) is (4 sin(4x - 6y), -6 sin(4x - 6y)).…

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Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: et…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (-1, 3)…

A: First find the parametric equation of line passing through the points (0, 0) and (-1, 3).

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Suppose that Vf(x, y, z) = 2xyze*i+ ze**j+ ye*´k. If f(0, 0, 0) = 5, find f(1, 1, 8). Hint: As a…

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Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

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Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, 2)…

A: C be the curve point (0,0) to (3,2) and (3,2) to (6,0) so, integral we need to compute I =∫c3dy-2dxI…

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: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Suppose that z = f(a, y) is differentiable at the point (1024, 1024) with, (1024, 1024) = 5…

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Q: 4. Prove that fer*dr+xydy = f, So*(y– 0)dydr where C is the triangular curve consisting of the line…

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Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

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Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

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Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: Compute F. dr where F (x, y) : (7xy + x cos x) i+ (-yev + 6x²) j and C is a piecewise closed curve…

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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: If L is the tangent line to the curve 7 (t)= (2t-1, t, t-2) at (3, 4, 2) and the point where L…

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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 a curve through the point (1, 9 whose length on the interval [1, 2] is given by i VI+ 25z!0dz-…

A: Explanation: Given a curve, ∫121+25x10dx Function f(x) has an arc length on the interval [a,b] is…

Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (-1, -2)…

A: Given: The curve C is the union of two-line segments, first going from (0,0) to (-1,-2) and the…

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: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

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Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the

A: Introduction: A line integral in calculus is an integral where the function being integrated is…

Q: Evaluate | xyzdx + In(xy)dy + xzdz over the straight line segment from (2, 1, 1) to (–1,1, –2)

A: We need to evaluate integral∫Cxyzdx+lnxydy+xzdz over the line segment from 2,1,1 to -1,1,-2.

Q: that F(x, y, z)= Divergence Theoren

A: The given vector field is Fx,y,z=xz2+12.13, sin y, x·y5. The upper hemisphere can be taken as…

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

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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.