Which of the following is a defining equation for the tangential plane to the surface defined by 2x²23 – 3xyz? + yz = 0 in the point (1,1,1)? Ox+2y+z=0 Ox+y-2z=0 O 2x-y-z-0 ONone of these. Ox-2y+z=0

Q: 1. Let k be a nonzero constant. Show that the equation of the tangent plane to the surface xyz = k…

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Q: Verify that the curve r(t) lies on the surface. Give the name of the surface. r(t) = (/3t cos t, V3t…

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Q: 1. Find the equation of the plane tangent to the parametric surface S defined by r(u, v) = uvi + u…

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Q: Which of the following planes is tangent to the sphere x² + y + z' = 17 at the point (2, -2, 3)? %3D…

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Q: An equation for the tangent plane to the surface : = (xty at the point P(1, 1, 4) is a) 8x + 8y -: =…

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Q: Consider the surface x2 + y2 − 2xy − x + 3y − z = −4 and the point P(2, −3, 18). Determine the the…

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Q: Find an equation for the tangent plane to the surface z = 6x3y2 + 3y at the point P(1, -3). Hint:…

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Q: 4. Let II be the plane tangent to the implicit surface x²y° + e²= = 5+ 2y sin(z) at the point (-2,…

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Q: Consider the equation of the surface S given by: ln(x2yz3) + xz − x2y = 0 An equation for the…

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Q: The parametric representation of the surface x² – 8x + z? = 0,0 < y < 5 is a) ř(u, v) = (4 cos u , 4…

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Q: Let (S) be the surface given by the following equation. x²+y² = 1+ z?. An equation of the tangent…

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Q: Consider the surface r²+y²+2ry-3x+2y-2z=1. Determine the following: (a) the general equation of the…

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Q: Let (S) be the surface given by the following equation. x²+y? = 1+ z?. An equation of the tangent…

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Q: Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 6) i+ (v³…

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Q: Consider the surface x2 + y2 − 2xy − x + 4y − z2 + 4 = 0 at the point Po (2, −2, 5). Determine the…

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Q: An equation for the tangent plane to the surface (xty at the point P(1, 1, 4) is a) 8r + 8y-:= 0 b)…

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Q: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

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Q: The parametric representation of the surface y2 - 4y + z2 = 0,0 < x < 3 is a) 7(u, v) = (v, 2 + 2…

A: solution:y2-4y+z2=0 , 0≤x≤3considery2-4y+z2=0∴y2-4y+4+z2=4∴y-22+z2=22

Q: The equation of the tangent plane to the surface yey +z =0 at the point (0,-1,1) is az+by+cz = 1.…

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Q: • What is/are the trace(s) of the surface (x – 1)? 22 = 1 on the rz-plane? 36 a. hyperbola b.…

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Q: 2. A surface S in R'(z,y, =) is defined parametrically in the form u + -1 -( ) X(u, e) = 2u 2 (a)…

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Q: Let (S) be the surface given by the following equation. x²+y? = 1+ z?. An equation of the tangent…

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Q: Let F (tanx + y)ĩ + (x + secy)j and C be the boundaries of the ellipse 9y=9 in the counterclockwise…

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Q: Show that the surfaces x2 + 2y2 + 3z2 = 3,   x2 + y2 + z2 + 6x − 10y + 14 = 0, are tangent to each…

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Q: Which of the following is the equation of the tangent plane of the z = 3x^2+x-y^2+y surface at the…

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Q: 7. Consider the Surface S:z = 52² + 5y?. An equation of the plane tangent to Sat the point P (3, 3,…

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Q: a. Find a parametrization for the hyperboloid of one sheet x2 + y2 - z2 = 1 in terms of the angle u…

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Q: Which of the following sets of parametric equations is for the surface obtained by rotating the…

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