{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2311_Test1PracticeSOLUTIONS_F11

# 2311_Test1PracticeSOLUTIONS_F11 - gow‘tteem Fall 2011...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: gow‘tteem Fall, 2011 MAC2311 Test 1 Practice Problems 1. A closed box must have width W = 12 inches, and its surface area must be S = 600 square inches. Write a formula that gives volume V as a single—variable function of length L. (333 gmmetry facts 01]'p,5) A Sezo~+aui+2ws VﬁLWE- \$2 2Lﬁi} +29% swim V: Maw HIV 'gzganutasawas VZEZL; we a as it, mam am we as s see m gas. =5 2. H < L +123 coo -=- 2% V: iZL< Zagreb) L wtllin a H i as w a; o saw-5m Lad” ‘2“) ﬂ I V “m” he‘l' recs“; moi . m I WW Tags? g Answer: V(L) : i L E2“ 2. The graph of piecewise~deﬁned function f is 3 shown for x 2 —4. Assume the ﬁrst piece is Y 5 semi-circular and the second linear. 5, (a 5) 4 1 a) Complete the formula for f . 3 (4’3) 1 auto) Wham?“ if—‘iéxé‘t ‘ “WWW ————e s 1H 12 ﬁx): Egg-"X44 if K>L§ » 28+ Ms M was Y; a (my (as? y \j 3%“ {WWW _ x1 ‘5! 351 fans“ _ w KWX WWW; M‘ﬁc a Eo‘i‘i‘bm remlwclmivsw r. Emi- l yaw—3 hmi ” :52; y; mm ymg a: E1 x v m» .L a a i {3.3 II w 3 m 1)) Evaluate each limit: lim f (x): ﬁg limf(x) x44" — 3: Sketch the graph of one possible function f(x) satisfying all of the given conditions. Label holes with both coordinates and asymptotes with their equations. x ; if; 0 domain off is (—oo,2)U(2‘,4)U(4,+oo) : - 332: male; f<x>=2 *: 4 twee-w and awe-{~00 : - 1};ng =1 “ 0 Graph is decreasing over the domain of f 0 Graph is concave down over (H003) U (2, 4‘) and concave up over (4,+oo) 4. Graphs of f and g are shown. Evaluate each limit. Showing work is not required. Graphoff ‘ _ ‘Graphofg a) 31332 f<x)= DNES b) 132m: —%~ w c) 133me I d) Elgg(x)= 2; 7 e) lim[4g(x)+5]= t) lim+ f(x) = Mia—m? x“ «93? g) Iim53/29+g(x) : 3 Jew->0 Y {3 x91 hﬁj W; 3—» 3i {E ‘ m b We _ 1 MW «- tisﬁ‘m 7;; “so w? i l . i E -. ' - 7 _ ‘\ mzwm Miami? miewgooo 3 ., "ﬁeuk‘qm Jon juggmﬂ 2. EH 5. Find each limit by any method. Partial credit will be awarded only if the answer is supported by Workbut showing is not required. Circle each ﬁnal answer. Val-M a) ENE—3 ‘W *3) Keo KW} Mlﬁﬁ‘mg‘lﬁﬂ “a? (See section 2.3 example 6) . _ a, r g. >4 aha «s; 3% :32; y m W a a a L Kemp K ‘2: \‘w' m e 3} K “a; wawme an+3w (see inverse trig summary on p.63) .431 . t We 4% MUC c) lin ace—x; gem C} Wmﬁﬁr M 91% “km”; a Xﬁm a iasuiee “’W‘aw‘» K “item ’ 6. Consider f(x)=—f:g—=mﬂ\$ ) her}? CloMaax Kg; Elilx\$a3g p x +x—6 ‘ (Wag—2) ﬁve a) Evaluate each limit: lim f (x): (egg. lim f(x)= é/g x4»? iim f(x)= @535“ xv~+73 b) Evaluate each 11m1t. xlirzn f (x) ‘5» OD f (x) Ob f (x) D l 0) Evaluate each limit: lim f ()5): lim f(x)= X214. xvi? ‘ {g a? x+w xa+w NW? ' m 7 ﬂ d) The graph of f has a hole at the point( “*3 , git}? ). E; m a l i {a «pm W W” E e) The graph of f has vertical asymptote x = 2?» KW gm 5 X KW E «wt-1A we a \$53M? \f :5 . f) Sketch the graph. Represent asymptotes using dashed lines, and label each asymptote with its equation. Represent the hole with a small open circle, and label it with both coordinates. _ is continuous. 7. a) Identify the x—axis interval(s) over which the function f (x) = 2 ' ' 4 —— x I m gsgmgaxa 7 must smegma. “that b) Identify the x—values Where f (x) = 1n(sin2 x) is discontinuous. Answer: mall’s?! ‘3 any .53??gi “gig? may ‘.a§W-viw~ §lnxe~rag 13;, {amalﬁamﬁéis s a mm k+cosx, ifx_<_0 8. Find the k—Value that makes f (x): 5Sinx _f >0 continuous at x='0. k: A; 1 t x M ' I _. im Ka-aasa a: lﬂw‘ve‘asﬁ a: gal ' l» Mm “xx-am” mar—5" 27> Kati-J amt aim? at: hm mg: a when a: 4;. Mama w”? 0+ X i ) gnaw 2' dials—a Ktiwso :Kaei g‘ mam K34) ¥{9)m g?” . f 3 ' WWW ii”) “M £0?) z: {(0) ‘35,) .Séff‘l’f’lg'gﬁimﬂ ﬁling dﬁ‘plhn’l*icym a? cominwéy >€m¥ C) 9. Consider f (x) = 1 In technology this is authored as 1/(1 + e A (1 / x)) . l+e%‘ I a) Evaluate each limit. mg} f(x)=© lim f(x)= V; ' I x—a ‘ x—>+oc a 12 : l l I a as “gum a . 7; _ was m.“ 3 1+ €4€gﬁeﬂm\$ 3_ \ b) If the graph has any holes, idenify them by giving both coordinates. (.0! Q ing (o g l‘} I c) If the graph has any asymptotes, identify them by their equations. \[ 1::- V2. ' Invefse Trigenumetric Functions 1 y=si11‘-x"c>x=siny where ~13x51 and W§Sysgw y=cos“1x<:>x=cosy Where —1Sx\$1 and ()3ny y=tan"1x<:>x'=tany Where -—oo<x<+<>o and ~§<y<§ y = 56071 x<2>x=secywhexexswlorx21andUSysyr,y¢ @Omejﬁ‘y Form Mag Rectangle with Length l. and Width Rectangular Box with Length L. Width W,l and Height H Area A = LW Surface Area A = ZLW +2LH + 2WH Perimeter P = 2L + 2W Volume V = LWH L. Triangle With Base b and Height 11 Sghere of Radius r 1 = 2 Area A = —-bh Surface Area A 4;” 2 4 3 _ Volume V m «53—17:? b P that mean Theorem C linder of Radius r and Hei ht h For a right triangle with legs a and b 2 2 Surface Area A = 22:?2 +2m'h and hypotenuse c, a +5 = (:2. w Volume V = 7:142}; W Right Circular Cone of‘Radius r and Height h Surface Area A = 71%.er +1112 . . h ' h I Volume V m a???" \‘zh 5 Area A m 7W2 Circumference C = 27:1“ ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern