EXERCISES 14.6 Tangent Planes and Normal Lines to Surfaces In Exercises 1-10, find equations for the (a) tangent plane a

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Exercises 14 6 Tangent Planes And Normal Lines To Surfaces In Exercises 1 10 Find Equations For The A Tangent Plane A 1 (49.37 KiB) Viewed 11 times

EXERCISES 14.6 Tangent Planes and Normal Lines to Surfaces In Exercises 1-10, find equations for the (a) tangent plane and (b) normal line at the point P, on the given surface. 1. x² + y² +2²= 3, P(1, 1, 1) 2. x² + y²2² = 18, P(3.5,-4) 3. 2zx²=0, Po(2, 0, 2) 4. x² + 2xy-y² +2²= 7, Po(1,-1,3) 7x - xy + ² + y2 = 4, Po(0, 1, 2) 5. cos TX 6. x²-xy-y²-z = 0, Po(1, 1,-1) 7. x + y + z = 1, P(0, 1, 0) 8. 2²+ y²-2ry - x + 3y -z = -4, Po(2,-3, 18) 9. x ln y + y ln z = x, Po(2, 1, e) 10. ye - ze=2, Po(0, 0, 1) In Exercises 11-14, find an equation for the plane that is tangent to the given surface at the given point. 11. z = In (x² + y²), (1,0,0) 12. z = ¹+ (0,0,1) 2 13. z 14. z = Vy-x, (1, 2, 1) 4x² + y², (1,1,5) Tangent Lines to Intersecting Su In Exercises 15-20, find parametri the curve of intersection of the surf 15. Surfaces: x + y² + 2z = 4, Point: (1, 1, 1) 16. Surfaces: xyz = 1, ²+2y= Point: (1, 1, 1) 17. Surfaces: x² + 2y + 2z = 4, Point: (1, 1, 1/2) 18. Surfaces: x + y² + z = 2₁ Point: 19. Surfaces: CO Point: (1, 1, 3) 20. Surfaces: x² + y² = 4, x² Point: (√2, √2,4) (1/2, 1, 1/2) x³ + 3x²y² + y²³ x² + y² + 2²: = 1 C