2. Find the equation of the normal line and the tangent to the parametric surface defined by the vector-valued function: R (u, v) = at the point (0, 2, 1)

Q: find a vector normal to the plane with the given equation. x − z = 0

A: Given: Plane: x-z=0 To Find: A vector normal to the given plane

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(2, - 1, – 5) for the funct 2x…

A: Given that  fx,y,z=ln2xy-z

Q: Find an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

Q: Sketch the level curve corresponding to c = 0 for the function given by           f(x, y) = y − sin…

A: We have given the function; f(x, y) = y − sin x This can be written as; z=y − sin x

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

A: We will find the equation of tangent plane to the given surface.

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

A:

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: Given: Surface f(x, y, z)=c and a point x0, y0, z0 To show: Equation of tangent line to f(x, y, z)=c…

Q: Find the equation of the tangent plane to the surface =1 16 at the point (1,-3,2) O a. 3x-2y+z=24 O…

A: Given: x24+y29+z216=1 x,y,z=1,-3,2. Simplify the equation.…

Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

Q: Consider the curve defined as r(t) = e^ti + e^tj + t k Determine the point on the curve where the…

A:

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: Find an equation of the tangent plane to the surface x = u² + 1, y = v³ + 1, z = u + v at the point…

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Q: Find the equation of the tangent plane to the parametric surface x = u², y = u- v?, z = v² , at the…

A:

Q: 4) Find the equation of the tangent plane to the surface r(u, v) = (u²-v²)i − (3uv)j + (4√u+v)k when…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

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 directional derivative of the function z(x, y) = In(x² + y²) at the point M(xo, Yo), in the…

A: The directional derivative of function z=fx,y in the direction vector u is calculated by the formula…

Q: Find an equation of the tangent plane to the surface represented by the vector-valued function at…

A:

Q: 2. Find the directional derivative of the function f(x,y,z) = xy? – 4x?y + z² at (1, -1, 2) in the…

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Q: Let C be the curve of intersection of the paraboloid x? + y² = z and the cylinder + (y – 1)² = 1. 4…

A: We will find equation of common curve and parametrize it to find vector equation of C and the use…

Q: a)What is the slope of the tangent line to the curve y=2sin4x  at x=⊼(pie)/4? b) Find a unit vector…

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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: Find the equations of (i) the tangent plane and (ii) the normal line to the surface z = excos(y) at…

A:

Q: The vector equation for the curve of intersection of the surfaces x = y² and z = y in terms of the…

A:

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(2, - 3, 11) for the function…

A: The unit vector normal to the surface f(x, y, z)=0 is ∇f∇f. where ∇f = fx, fy, fz and ∇f = fx2 + fy2…

Q: Find the unit tangent vector and the parametric equation of the line tangent to the given curve at…

A:

Q: find the derivative of f(x, y) = x² + xy at P,(1,2) in the direction of the unit vector u = i+ V2

A:

Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

A:

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

A: Given that: f(x,y)=x2y at the point (1,1) Ellipse: x2+2y2=1 at the point (1,0)

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

A:

Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…

Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1, y = v + 1, z = u + v at the…

A:

Q: Choose the normal vector of the tangent plane to the surface defined by Z = e6x²+14xy-5y² at the…

A: To find: The normal vector of the tangent plane to the surface at the given point. Given…

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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

A:

Q: Let P be the point (2, -1, 2) and Ø,: x² + y² – z² = 10. (i) Find the unit normal vector to the…

A: (c) The given surface is ∅1: x2+y2-z2=10 and the point P: 2,-1,2. (i) The unit normal vector to the…

Q: Find a unit normal vector to the surface at the given point. x²y3 - y?z + 2xz3 = 4 (-1,1, –1)

A:

Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the…

A: Explanation of the answer is as follows

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 the tangent plane and normal line equations to x+y +z =1 at the point (1, %3D -2, -4).

A: This question is related to 3D geometry and equations of plane and lines,  we will solve it using…

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

A:

Q: (b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane %3D z = 0.…

A: As per our guidelines, we can only solve first question and rest can be reposted. The solution for…

Q: Find an equation of the tangent plane to the surface z = xy at (1,2,2).

A: The given surface can be written as F(x, y, z)=0, where F(x, y, z)=xy-z

Q: Find the equation of the tangent plane to the surface xy + 2yz + 3zx = 11 %3D at the point P (1, 1,…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z = V xy, (2, 2,…

A: