mthsc206-fall-2010-notes-15.4

mthsc206-fall-2010-notes-15.4 - 15.4 Tangent Planes and...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 15.4 Tangent Planes and Linear Approximations Tangent Planes and Linear Approximations Definition 15.4.1 Let z = f ( x, y ) determine the surface S . If f has continuous first order partial deriva- tives at ( x , y ) , then the tangent plane to the surface S at a point P ( x , y , z ) is the plane that contains the point P and the tangent lines to the curves of intersections with the vertical planes x = x and y = y at the point P . Is there a general formula for the tangent plane at a given point? Lets see. The point P ( x , y , z ) is the point on the plane. In the plane y = y , the tangent line to the curve of intersection has para- metric equations x = t, y = y , z = f x ( x , y )( t- x ) + f ( x , y ) , and the tangent line to the curve of intersection in the vertical plane x = x has parametric equations x = x , y = t, z = f y ( x , y )( t- y ) + f ( x , y ) . Problem: Find a normal vector to the tangent plane containing the two tangent lines given above, and then, find an equation of the tangent plane.then, find an equation of the tangent plane....
View Full Document

This note was uploaded on 10/11/2010 for the course MTHSC 206 taught by Professor Chung during the Fall '07 term at Clemson.

Page1 / 2

mthsc206-fall-2010-notes-15.4 - 15.4 Tangent Planes and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online