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worksheet 10

# worksheet 10 - Math 200 Spring 2010 Worksheet 10 Name K23...

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Unformatted text preview: Math 200, Spring 2010 Worksheet 10 Name K23 Section 14-1 Functions of Two or More Variables 1. Find the domains and ranges of the following functions and sketch their domains. (a) f(x,y)=\/1+x-y2 (b) f(x,y)= y-xln(y+x) (C)g(y,2)= 1 Hy: (d) P(r,s)=e \+x—723_0 :9 xzyl—l 7-) 20 w y+x>o ”ﬁnal are} ml“ 0 z? eff \I 2 X ““4 X} '7 1 +LQ. Y's-ohm? ‘ 0 = {(3 )) 2 #— é wok the r—oms 2‘! f / 1y, ,, Jammie! (If: sin/ﬂ) s ”s Wine #1:me R“)? l (”‘3‘”) mm segment it») 2. Sketch the vertical and horizontal traces for f (x, y) = 9 —— x2 — y2 . - The hart-zon'lul +Nue oc’l‘ heibkl-c; '. q_x1_y2:(_ xii-y" = ‘i~c. Circle (enkréb o) rudgus r‘: \Iq—C ~71? V'ri‘w‘ i“? "V‘ ("M9 “R'- 2: (“t—of)“; ‘3 q Snowbolc‘ openﬁu] downward! 1. -Tl\e veriﬁed 'l‘mce ﬁg {ll-0mg ’19,: 2-: (ol-lv-z)-X Us c. @tholm OPEN-t5 downward 3. Draw a contour map of the function showing several level curves. (3) f(x,y)=x3—y (b) f(x,y)=y/(x2+y2) (C) f(xsy)=ey!x ”A c :C Far C 70 and (7‘15) 5“ {0,0} level curve! 1 =9A~C x C: £22,: =>i<1+31~3é=0 7311"“: 7L+ 3 "_J__ For c7|)+oa.chueI . ‘2 (7-5; we“ we 9m; “max “E310 °~ finned“; BF Circle] Fur £31 Mule ”’09" W“)? m cart». (Gun) om; radon] is mix—axis. Usfna cowl-ow tri'QTW-lc'Z‘S-g -ﬁ 4. Sketch both a contour map and a graph of the function f(x,y)=\/m The (Oh‘l'ouv’ map Consisl's log-Poe lQle curve: C =1l‘ge..qx1,.L+7\. 1 . . <79 Qx+‘r‘=3€-c",czo boi'uclx )5 q ‘Pamil: G {’1le591 tut-HA maxi" 0.315 -H~e \rmcts. 5. Make a rough sketch of the graph of f that has the following contour map. 6. (a) Use Winplot to graph the “monkey saddle” function f (x, y) = xy2 — yx3 . (b) Use Winplot to plot some contour lines of this function and compare with the graph. 7. Locate the points A and B in the map of Lonesome Mountain. How would you describe the terrain near A? Near B? Near Pr Hm Hue! Curve! are close "l'baei-‘her inéx‘ewi-u-a \$H¢p +9Tr'cuy. Necw 8 He level Cuwe: are muck Mr. qpqn'l thdtcm‘hna MUCL [991 sl—eef term», parka.“ 419,-! 9. Find and sketch the domain of the function f (x y, z) = ln( ‘F 15 deﬁne; when. lB“‘-}-xl—I-1.7L.—QL>O _>,.+¥_1+%‘_EL<I TL“) 9: 31* [293,211 ‘3‘"?th 1E Homework #10 Reread Section 14.1 8. Compute the average ROC from A to the points B, C, and D. Huerqae ROC 9101'; nae = fig—ﬁt!» Quanta-e REC prom :292 5 .3? A “C Set: 6 HUQtuae ROC—0 £70m ﬁ'h 0 T— 260 : O 9. L 16 4x2-4y2—z: He feud-5 instole +le elhmeJ ,. B' ‘ Cr \ Function does not change A {—1 8 along the level curve A L~—---—-—I C Contour interval: 100 ft Horizontal scale: 200 ft um. FIGU R E 17 Contour map of mountain. (Due 3/5) Do Section 14.1 Exercises: 7, 13, 15, 17, 19, 20, 21, 23, 29, 37, 39, 40, 41, 44, 47- 54(a11) Prepare for next class session: Read Section 14.3 (Skip Section 14.2) ...
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worksheet 10 - Math 200 Spring 2010 Worksheet 10 Name K23...

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