1. a) Find equations of the tangent plane and the normal line to the 2(x - 2)² + (y-1)² + (z-3)² = 10 at (3,3,5). b) Find equations of the tangent plane and the normal line to the xe²y-z + x² = yz-2 at (-1,1,2). 2. Find all points, if any, on the paraboloid y = 1 of 3 x² + z² where the tangent plane is parallel to the plane x + 2y + 3z = 1. O =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1:04 0⁰
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1. a) Find equations of the tangent plane and the normal line to the 2(x − 2)² + (y − 1)² + (z − 3)² = 10 at (3,3,5).
b) Find equations of the tangent plane and the normal line to the xe²y−z + x² = yz — 2 at (−1, 1, 2).
1 of 3
2. Find all points, if any, on the paraboloid y = x² + z² where the tangent plane is parallel to the plane x + 2y + 3z = 1.
91%
O
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Transcribed Image Text:1:04 0⁰ - 1. a) Find equations of the tangent plane and the normal line to the 2(x − 2)² + (y − 1)² + (z − 3)² = 10 at (3,3,5). b) Find equations of the tangent plane and the normal line to the xe²y−z + x² = yz — 2 at (−1, 1, 2). 1 of 3 2. Find all points, if any, on the paraboloid y = x² + z² where the tangent plane is parallel to the plane x + 2y + 3z = 1. 91% O |||
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