Consider z as a function of æ and y and z = Ax + By + D be the tangent plane to f(x, y) = 2a² + 2y³ + 5xy+ 2x + 3y at (3, 3). What is the value of z at (3, 3)?

Q: Find the equation of the tangent plane to z = f(x, y) at the point (1, , 1).

A: Given Data: Surface: z=x2esiny Point: x0, y0, z0=1, π, 1   (a) The first derivative of the given…

Q: 4. For the function f(x,y) = 2x² – 3xy + 8y? + 2x – 4y + 4, find a tangent vector to the level curve…

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Q: Find the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent…

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Q: Verify Stokes's theorem for F =, where C is the curve C: x² + y² = 4, z = 2

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Q: 1) For f(x,y, z) = x² – (1 – y)² + z². Find directional derivative of f at P(1,1,1) in the direction…

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Find the tangent plane for the level surface f(x,y,z) = 5x4 + cos (4y) + In (6z) = c at the point…

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Q: 1) For f(x, y,z) = x2 – (1 – y)? + z?. Find directional derivative of f at P(1, 1, 1) in the…

A: Given that  f(x,y,z)=x^2-(1-y)^2+z^2 Point P(1,1,1) Vector is a=(0,3,4)  To find the directional…

Q: Suppose given a function f(x, y, 2) of three variables, and a point (o, y0, 20) €R. Explain in your…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: Find an equation of the tangent plane at P = (0, 3, – 1) to the sur- face with equation ze* + ez+1 =…

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Q: Find the derivative of ƒ(x, y, z) = xyz in the direction of the velocity vector of the helix r(t) =…

A: Concept: A vector is a directed line segment whose length is the magnitude of the vector and with an…

Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

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Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

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Q: Let flxiy) = Rx Jy 27 %3D a) Finid the gradrent of f b) Find the directional derivative of f at the…

A: Consider the function as  fx,y=2xy

Q: The tangent line to the curve r(t) =(t°,t“, t³ ) at the point (1, 1, 1) intersects the æy-plane at a…

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Q: Find an equation of the plane tangent to the following function at (0, 0): O z = 9 O 2x +2y+z-7=0 O…

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Q: Find the directional derivative, Dvf , of (*) f(x, y, z) = 4x tan 1 at the point P = (1, 1, 1) in…

A: To find the directional derivative of f(x,y,z) at P=(1,1,1) and the Direction, v=(1,2,2).

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

A: To find the equation of the tangent plane to the surface z=ln2x+y at the point -1, 3, 0.

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈1 − t^2, 5t, 2t^3〉, t = 2

A: r(t) =(1-t2, 5t, 2t3) at t=2

Q: Find one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).

A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…

Q: Let f(x, y, z) = 3ex cos(yz). a) Find the directional derivative of f at P(0, 0, 0) in the…

A: Given , fx,y,z=3ex cos4zwe have to find directional derivative of f at p 0,0,0 in the directionof…

Q: Find the point on the graph of z = 3x2 + y at which vector n = (24, 2, –1) is normal to the tangent…

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Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

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Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: Find the tangent plane for the level surface f(x,y,z) = 3x5 + cos (5y) + In (5z) = c at the point…

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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: Consider the function f(x, y) = 2xy + x2 + 5 Find the equation of the tangent plane to the surface…

A: given: f(x,y)=2xy+x2+5 find the equation of tangent plane to the surface z=f(x,y) at (-1,1,4)

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 derivative of f (x, y,z) = xyz in the direction of the velocity vector of the helix…

A: Answer and explanation is given below...

Q: Compute the directional derivative of f(r. y) = = at the point (1, 1) in a irection normmal to the…

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Q: Find an equation for the tangent plane of z 3.xy? + y + 2 at the point (-1, 1, 0).

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Q: Find the directional derivative Du f(-3/8,1) for the function f(x, y) = cos(T(4x + 2y)) in the…

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Q: Compute the plane tangent to the graphs at the indicated points using the given functions. (Let z be…

A: Note : As per the authoring guidelines, when multiple subparts are posted, only first 3 subparts or…

Q: Consider z = Ax + By + D be the tangent plane to f(x, y) = 2x² + 5y³ + 9xy + 9x + 3y at (6,9).What…

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Q: Find the tangent plane for the level surface f(x,y,z) = 7x5 + cos (5y) + In (9z) = c at the point…

A: Answer: In oerder to use gradients we introduce a new variable c= 7x5+cos(5y)+ln(9z) Therefore the…

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

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Q: Find the tangent plane for the level surface f(x,y,z) = 7x³ + cos (4y) + In (4z) = c at the point…

A: Tangent plane for the level surfacefx,y,z at (a, b, c) is…

Q: Compute the directional derivative of f at the given point in the direction of the indicated vector.…

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Q: Compute for the directional derivative of f (x, y, z) = tan (Tx – 21ny)e4y-z at the point (, 0, In…

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Q: A curve is given by the parametrization r(t)= [²,-t, ť ]. If the tangent vector to this curve at a…

A: The given curve is,  ,

Q: Find the tangent plane to the function f(x, y) = sin(xy?) at (a,. Is it parallel to the plane 2x- 3y…

A: fx, y=sinxy2 Partially differentiating with respect to x, we get fxx,…

Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, Yo: 20) is given by the…

A: This is the question from vectors.

Q: If the gradient of f is Vf = x³ } – zỉ+ 2yx k and the point P = ( surface f (x, y, z) = 0, find an…

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Q: Consider z = Ax + By + D be the tangent plane to f (x, y) = 5x² + 10y³ + 6xy + 8x + 7y at (-0, 4).…

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Q: (b) Find the directional derivative of the function f(x,y,z) = xy sin z at the point (1,2, %3D T2)…

A: Solution:

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

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Q: Find the equation of the tangent plane at the point x = ¤0 =4, y= yo == f(x, y) = xye²+y Select one:…

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Q: For the surface f(x, y, z) = 2*yz, find: The derivative at the point (1,2,1) in the direction of v =…

A: To find the derivative  of the given function f(x,y,z) at point (1, 2,1) in the direction of vector…

Q: Let f ( x , y ) = 2 x − y + x2 + y4. Which (unit) direction vector u  MINIMIZES the directional…

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Q: (1) Let f(x, y) = xe" + x2. (a) Find the tangent plane of f at the point (2,0). (b) Use your answer…

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