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3-12 Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. パ+?+= 25; P(-3.0,4) 1.ニ r %3D 4. x²y-4z2 =-7; P(-3, 1,-2) 56; P(-4, 5, 2) バ 7 5. x-xyこ 6. z = x² + y; P(2,-3, 13) 7. z = 4x'y + 2y: P(1,-2, 12) 8. z = xy2; P(2,4. 4) 9. z xe; P(1,0, 1) 10. z = In x2 + y?; P(-1,0, 0) %3D 11. z = ey sin 3x; P(7/6, 0, 1) 12. z = x/2 + y/2; P(4, 9, 5) %3D %3D 26. Find all points on the ellipsoid 2x2+ 3y² +4z = 9 at which the plane tangent to the ellipsoid is parallel to the plane x %3D 2y + 3z = 5. 21. Find all points on the surface x2 + y² z2 1 at which the normal line is parallel to the line through P(1,-2. 1) and Q(4, 0,-1). %3D

3-12 Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. パ+?+= 25; P(-3.0,4) 1.ニ r %3D 4. x²y-4z2 =-7; P(-3, 1,-2) 56; P(-4, 5, 2) バ 7 5. x-xyこ 6. z = x² + y; P(2,-3, 13) 7. z = 4x'y + 2y: P(1,-2, 12) 8. z = xy2; P(2,4. 4) 9. z xe; P(1,0, 1) 10. z = In x2 + y?; P(-1,0, 0) %3D 11. z = ey sin 3x; P(7/6, 0, 1) 12. z = x/2 + y/2; P(4, 9, 5) %3D %3D 26. Find all points on the ellipsoid 2x2+ 3y² +4z = 9 at which the plane tangent to the ellipsoid is parallel to the plane x %3D 2y + 3z = 5. 21. Find all points on the surface x2 + y² z2 1 at which the normal line is parallel to the line through P(1,-2. 1) and Q(4, 0,-1). %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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equations for the normal line to the surface at the point P. 3-12 Find an equation for the tangent plane and parametric 3. x+ y? + z = 25; P(-3,0, 4) M,= EK yr 2 4. x²y-4z =-7; P(-3, 1,-2) %3D 5. x - xyz = 56; P(-4, 5, 2) 1-17 6. z = x? + y2: P(2,-3, 13) 7. z = 4x'y2 + 2y; P(1,-2, 12) 8. z = x'y2; P(2,4.4) %3D %3D 9. z xe; P(1,0, 1) 10. z = In x2 + y2; P(-1,0,0) 11. z = ey sin 3x; P(7/6,0, 1) 12. z = x/2+ y/2: P(4, 9, 5) 26. Find all points on the ellipsoid 2x + 3y² + 4z = 9 at which the plane tangent to the ellipsoid is parallel to the plane x 2y +3z 5. 21. Find all points on the surface x2 + y²-z 1 at which the normal line is parallel to the line through P(1,-2, 1) and Q(4, 0,-1). %3D the sphere
Transcribed Image Text:equations for the normal line to the surface at the point P. 3-12 Find an equation for the tangent plane and parametric 3. x+ y? + z = 25; P(-3,0, 4) M,= EK yr 2 4. x²y-4z =-7; P(-3, 1,-2) %3D 5. x - xyz = 56; P(-4, 5, 2) 1-17 6. z = x? + y2: P(2,-3, 13) 7. z = 4x'y2 + 2y; P(1,-2, 12) 8. z = x'y2; P(2,4.4) %3D %3D 9. z xe; P(1,0, 1) 10. z = In x2 + y2; P(-1,0,0) 11. z = ey sin 3x; P(7/6,0, 1) 12. z = x/2+ y/2: P(4, 9, 5) 26. Find all points on the ellipsoid 2x + 3y² + 4z = 9 at which the plane tangent to the ellipsoid is parallel to the plane x 2y +3z 5. 21. Find all points on the surface x2 + y²-z 1 at which the normal line is parallel to the line through P(1,-2, 1) and Q(4, 0,-1). %3D the sphere
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