MATH 1XX3 Lecture Notes - Lecture 28: Tangent Space, Calix Inc., Hyla

• School: McMaster University
• Department: Mathematics
• Course: MATH 1XX3
• Professor: Adam Van Tuyl

Document Summary

Goal : generalize the idea that near function on a y= flx) near. Tangentplanesllinearttpproximatio the function looks like a plane the function a point. 7- fcx the function looks like a line . Set up : let s be a surface defined by zfcx , y) fxlx , g) At point d= ( x fxlx , g) is the slope of the parallel of the tangent line parallel x . axisfylx ,g) is to the tangent line the slope to the y . axis. Definition : the tangent plane to the surfaces at the point. Plx , g , fix ,yd is the plane that contains both of the above tangent lines. If f is continuous with partial derivatives fx and fy then the equation of the tangent plane at point p= ( xo , yo , Z - zo = fx ( x. , g. ) ( x. Xd + fylxo , yo ) ( y - g. )