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# MAT 211- Lecture 3 MAT 211

ASU

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This 4 page Class Notes was uploaded by Brigette Maggio on Friday January 29, 2016. The Class Notes belongs to MAT 211 at Arizona State University taught by Dr. Mohacsy in Fall 2015. Since its upload, it has received 25 views. For similar materials see Math for Business Analysis in Math at Arizona State University.

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Date Created: 01/29/16

MAT 211 Lecture 3 Section 15.1 (Cont.) Position of Two Planes in the xyz plane can: be parallel OR intersect in a line (called a line of intersection) Ex.: At which line the plane z= 3x2y+6 and the yz coordinate plane intersect? yz coordinate plane> x=0 z= 2y+6 Ex.: At which line the plane z= 3x2y+6 and the xz coordinate plane intersect? xz coordinate plane> y=0 z= 3x+6 Ex.: At which line the plane z= 3x2y+6 and the xy coordinate plane intersect? xy coordinate plane> z=0 z= 3x2y+6 Ex.: Homework Problem #13.) z= f(x,y)= 13x+2y xint.: y=0, z=0 0= 13 x= ⅓ (⅓,0,0) yint. z=0, x=0 0= 1+2y y= ½ (0,½,0) zint. x=0, y=0 z= 1 (0,0,1) 2 2 2 2 Ex.: z= f(x,y)= x+yFind the graph of the function z= x +y. a.) At which curve the surface z= f(x,y)= x2+y and the xz coordinate plane intersect? y=0 z=x+y 2 z=x>curve of intersection 2 2 b.) At which curve the surface z= x +y and yz coordinate plane intersect? x=0 2 2 z= x+y z= y> curve of intersecti (creates a paraboloid) Ex.: At which curve the surface z= x2+y and the plane z=y intersect? z= 4 z= x+y 2 2 4= x+y>circle 2 2 Ex.: f(x,y)=√ 1 − (x + y ) zint: x=0 & y=0 z= 1 − (x + y √ z= 1 =− 1 z= 1 (x+y) 2 2 2 x+y+z= 1 sphere radius= 1 center= (0,0,0) z= √1 − (x + y ) lower semisphere 15.2 Partial Derivative of z= f(x, with respect to x is the derivative of z= f(x,y) with respect to x. When y coordinate is fixed, Notation: sigma f/ sigma x (or fx) rate of change of z with respect to x when y is fixed

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