Chapter 9.1 Functions of Several Variables Oct 7, 2019 6_57_38 PM.pdf

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1 variable flx 3 x 2 variables f x y 3 7 y Funchonof2varia let D be a set of ordered pairs of real numbers to each pair X y in D these corresponds a unique real number 2 IX y then f is called a function of X y The set D is called the domain of F The corresponding 2 Values is called the range of f f z 2,3 f 2,3 14,5 f 4,5 flxth Hx slope h Examples Evaluate I f X y y2 f 3,2 1312 7127 537 2 flx y z e ly z f 10 1,4 e I 11 1411 3 3 flx y 4x 2 y q flxth.yj f.li h
flxth y 4 Xth Ly 41 2 2 4 th Ly 14xltoxht4h2 p.ly x y1 4lx't8xht4h h2 4xY2 8xhnt 4h2 ht 8 1 4h Graph of a function of 2 Variables 2 yo yo Zo y f Lxo Yo x Plant The graph of ax by to 2 D is a plane if a b c are not all zeroes 4 Plot the points d 0,0 4 b I 2 0,0 E 0,3 O d 1,2 51 n i f i 5 Graph Xtytz S O O 5 O S O IS 0,0 as a tin
e n 6 Xt y 4 10 4 14,01 l I i T No Z intercept therefore the plane is parallel to Z axis 7 Yt 2 5 10,51 15,01 a A Parallel to x axis 8 X S S O O r a r i il i i levelcurvest

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