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Unformatted text preview: MAC 2233: Exam '3 'IULTIPLE CHOICE. Choose the nne alternative that beat enmpletes the statement or answers the questinn. t+2 1} DiffEJ'EJ‘JtiﬂfEIB H Inﬁll I _ t 3.1;
A} {.1 + 2}nd — 1} [r — I]
II {I + 2;!{1' + 3) @I + 2
E] mme (If the above ind Fix} fer the fellnwing function.
2; m = 95K: + t A111”an + I 3(?I.12) C) J 3(1411'12} @ZFH? In 2] [3x — 4} In 1D {3x — 4}1r1 10 I3} + {3 Inﬁxj] @ x5[1 + f] 111(3):]:1
.7 Find the antiderivative.
e; fissi— a) as A} 5x2 _ as + C
_ 3E3}
HUI—.311};
r.
A} 3831 + C Find f”{ ] fer the folio 'n funet'on. 1' 3 ‘ _i_.__
"H_,,__‘"“sg 1 5:061 ‘
Ii} its} —.7 inﬁh— I} 2'43 243 ' '
—— Bi— (:1 . D] .
® {9X_I],2 {gx_n2 ELK—1 931—1 PM):  27(sxg)“2(‘i) : '2‘805’394 l3} six (9 ass5K D] —25e5x if 5 g}:
"F (0:963. if'5 :: 2 5:3
SHORT ANSWER. Show all wnrk CLEARLY. Write your answer in the space prnvided. Unless ntherwise instructed, gi
exact answers. . i if
12; Ha} =e5" : (15“, 5 : 5&5 A} seﬁk Differentiate.
13} y = In [in {in 5x3] [Fpﬂints] SHORT ANSWER. Shaw all wnrk CLEARLY. Write y‘aur answer in the space provided. Unless ntherwise instructed, gi
exact answers. out” n
Differentiate. 13} y=n [111(11‘13xj] [Fpﬂinis] “*1. [13 painis] Find the requested value {if the secand derivative {if the function. Give the exact value. 15) ftai=4e‘*2; (a) Find it} rear: {it} ma}. (b) Determine ivhether the graph Hi: ﬁx} is; inereaeing, LiE‘CJ'Erlﬁillg a'n' turriirig at x = 4.
hi} Determine whether the graph Hi: ﬁx] is enneave Lip, L‘L'Jrieave Lh'nvn a'n' neither at a: 4. [13 paints] )8" 'a = r36 +[~‘3x) (:2 xe‘T‘ v _ 1 ﬂ? _
306$ ‘* ~3e‘“+1éx1c,x he): ~stvue'“’ <0 {a} (i) PH] = At a = LL the graph til: i5
{b}{increaﬁilig,."Lieel'eaai1'ig} [{2} {Ct'}ltCr1‘i"it}’] MAC 2233: Exam 3 Find Fix} and f” {x} fur the fnlluwing functinn. Simplify ymu‘ answer. In; my =x5e‘h __ g 6 [15 points]
u u  a
u ‘ ‘U‘ : 6'” I — f I .
«Cm __. marlmu ._ _SK_L€_1X_+ 5‘ ¥TFL$);ufv+qu+ VT W
“r N—(——‘
7C6): 3 D X46 Xi‘ *SX'L. Find the equatinn in slope—intercept farm of the line tangent tn the curve at the indicated paint. Give exact numbers. [9 points] 34:0 MAC 2233: Exam 3 Integration When performing inTegroTion/onTidifferenTioTion, follow This order:
1. RecogniTion (o1c whoT funeTion is The expression o derivoTive?) 2. Power Rule (reverse of The power rule for derivoTives) 3. SubsTiTuTion meThod 4. InTegroTion by PorTs. NoTe: Eoeh sTep ineorporoTes The previous sTeps. P236) '2 GOV“) Integration by Substitution  Used to perform ontiderivotives thot do work by recognition or Power Rule.
 Usuolly opplies to composition of functions and some products.
 Is loosed on the reverse of the Choin Rule. ‘01? g—l—AMLG’): g( 
_ w}
9 ‘46!“ : Dix 51.2.9 0.5 1 I'd; U: L? {IiI g. I i d d'
3;“ u: I x “=9 3du:3xa{x a 0.5;?
E '3 J 2 8” Fr L" 3 C .._ '5' I
 3 +1 ——————I—=h: ...
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