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A: To find:
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Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!
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find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of f(x,y,z)=x-y-z.
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- Solve for the distance between the point P(0,0,0,0) and the plane w + x + y + z = 3 in R^4.Sketch the surface x = 2y2 +3z2The equation of the tangent plane to the surface at the point (-2, 1, 3) is Select one: 8 +2y- = -(x-2) + 2(y + 1) - (z + 3) = 0 -(x + 2) + 2(y-1)-(2-3) = 0 -(x + 2) + 2(y-1)-(2-3) = 2/ z-3 x1/2 = 22² =222332 -2/3 None of them 3
- Sketch the surface with equation x^2 + y^2 + 2z^2 − 1 = 0.Find an equation of the tangent z = 4x² - y² + 2y, plane to the given surface at the specified point. (-2, 4, 8)Find the equation of the level surface of the function g(x,y,z)=x^2+y^2+z^2-2x+4y-6z corresponding to c=2 and describe the surface if possible.
- Find an equation for the tangent plane to the surface z = 3y^2 − 2x^2 + x atP(2, −1, −3). Express your answer in the form z = ax + by + c.Find the tangent planes to the surfaces given by the equations z = 7x^2 - 12x - 5y^2 and xyz^2 = 2 at the point P(2, 1, -1), and show that the planes you find are perpendicular to each other.Curves (x- 1) (y- 2) =5 and (x - 1)^2 +(y + 2)^2= r^2, intersect at four points A, B, C and D. If centroid of tri(ABC) lies on line y = 3x- 4, then find the locus of point D.
- Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)Write the level surface 5=5x+y^2+sqrt(z) as the graph of a function f(x,y). f(x,y)=For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which passes through the point (1,1,12) and perpendicular to the given surface