48. Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point (a) (1,0, 2) (b) (-2, 4, 1) (c) (0, 0, 0).

Q: Sketch the section of the surface at y = 0. 2x + z = 3 4 -8 -6 -4 2/4 -2 6 8 -6 -8- 6. AM -8 -6 -4-…

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Q: The slope of the surface z = xy² in the x-direction at the point (2, 3) is _____, and the slope of…

A: Given:z=xy2   x-directionat the point 2, 3 y-directionat the point 2,3

Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

Q: Find the equation of the plane tangent to the surface G(x,y, z) = 2x² - y² – 3z2 = -4 at P = (-2,…

A: Given surface is                                                G(x, y, z): 2x2-y2-3z2=-4 we have to…

Q: Find the equation for the tangent plane to the surface Z =-8x² - 3y2 at the point (2 1, -35). O 2x +…

A: We can find the answer as below

Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

Q: Determine equation of tnagent line to the common curve of 2 surfaces w/ equations: z = x? + y – 2xy…

A: follow next step

Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 3 at the given point( 2, 1, 8).

A: Known fact: Let F(x,y,z) be the surface which is differentiable at P(x0, y0, z0). then the equation…

Q: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

Q: Picture attached. Thanks in advance!

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Q: Determine if the surface x^2 + y^2 +z^2 = 1 is tangent to the surface x^2 + y^2 + z^4 = 1 at…

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Q: Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point (a)…

A: Given: fx,y,z=xyz+3 Let fx,y,z=xyz+3 the level surface are given by, xyz+3=k        ,k∈ℝ…

Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Show that the line normal to the surface xy + z = 2 at the point (1, 1, 1) passes through the…

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Q: Find the equation for the tangent plane to the surface z= 7x2. 10y² at the point (2, 1, 18). O 2x +…

A: Equation for the tangent plane to the surface z=f(x, y) at the point (a, b, f(a, b)) is given by

Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

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Q: The equation of the tangent plane to the surface X +y- z = (2, –1, -1) is 2 at the point | O a) None…

A: This question can be solved by applying the formula of equation of tangent plane to the given…

Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

A:

Q: Find and classify all the critical points of the surface with its equation z = 3x"y + y* – 3x2 – 3y?…

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Q: 4. Find an equation of the tangent plane to the surface z=- xy+8 at the point (1,1,-10) ху — 2х

A: Equation of tangent plane is: {df(x0,y0)/dx} (x-x0)+{df(x0,y0)/dy} (y-y0)-(z-z0)=0

Q: What kind of surfaces are the level surfaces f(x, y, z) = const? f = 4x - 3y + 2z

A: As per the question we are given a trivatiate function : f(x, y, z) = 4x - 3y + 2z And we have to…

Q: (b)Let f(x, y) = /3x +2y. %3D Find the slope of the surface z = f(x, y) in the x-direction at the…

A: (b) Slope of z= f(x,y) in the y- direction at the point (4,2) Slope ofz in the y - direction means…

Q: 2. Sketch the level surface of the function w = f(x, y, z) = 25 – x² – (z – 2)² for w = 9.

A: 2. Sketch the level surface of the function w=fx,y,z=25-x2-z-22 for w=9.

Q: Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

A: Follow the procedure given below.

Q: Calculate SS dxdy D (x+y)² in Surface D limited to curve y=x² and the lines 2 Y=x+2 and x = 1.

A: Given:  integral ∫∫Ddxdy(x+y)2  in the surface D limited to curve y=x2 , y=x+2, x=1  To Find : value…

Q: What kind of surfaces are the level surfaces f(x, y, z) = const? 9. f = 4x – 3y + 2z 11. f = 5x² +…

A: (13) Given  f=z-(x2+y2)     Level surfaces ,   f(x,y,z)=C   (constant) i.e z-(x2+y2)=C i.e…

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Consider M is the mass of the triangular plate bounded by the y-axis and both the lines. To find…

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given:- The equation of the surface revolved for the x-axis is, z2-xz=ln(x)+3x

Q: 4. Parameterize the curve of intersection of the surfaces z = x² + y² and y² + (z – 1)² = 1.

A: parameterisation

Q: (b)Let f(x, y) = / 3x + 2y. Find the slope of the surface z f(x, y) in the x-direction at the point…

A: Slope of z= f(x, y) in the y- direction at the point (4,2) Slope of in the y - direction means…

Q: Find the equation of tangent plane to the surface x² + 2y? + 3z2 = 21 which is parallel to the plane…

A: Topic- equation of tangent to surface

Q: What kind of surfaces are the level surfaces f(x, y, z) = %3D const? 9. f = 4x – 3y + 2z 10. f =…

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

Q: The slope of the surface z = xy2 in the x-direction at the point (2,3) is ______, and the slope of…

A: Given, surface, z = xy2Differentiating the z with respect to x assuming y as constant,∂z∂x = y2×1 =…

Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: We have to solve given problem:

Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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Q: 5) Consider the surfaces S1 : ryz = 10 and S2 : z =r² + y and the %3D point Po = (1,2,5).

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Q: a) Compute the equation of the tangent plane to the level surface 9(x, y, 2) = x’y + 2y°z – 3z°x = 3…

A: First we calculate gradient of g(x,y,z) at point (1,0,-1). Then find equation of tangent plane.

Q: The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

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Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0< x <1…

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Q: (b)Let f(x, y) = /3x +2y. Find the slope of the surface z = f(x,y) in the x-direction at the point…

A: It is given that, f(x,y)=3x+2y. It is known that the slope of any function is defined as,…

Q: Find and classify all the critical points of the surface with its equation 2 = 3a²y + y3 – 3x² – 3y?…

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Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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Q: Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your…

A: Solution:

Q: Find the equation of the tangent plane to the surface 4. =1 at the point 16 9. (1,-3,2) O a.…

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