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Unformatted text preview: +l ix; . loo /m U Student Name: I prim; .. m. (ht ' “EL/m 9 Sections 2.5 (Due: Tuesday, 09l0 ) _ . 1",‘C/agi HOW VJOF K “I C‘Q\VCL\lS lLQXi’ V‘lm
Description: This homework emphasizes the graphical and mathematical
deﬁnitions of continuity. it is important to know when the function is discontinuous
and how to apply the intermediate Value Theorem. Show all work to get full
credit.
1) If f is continuous on (00, no), what can you with certainty say about its graph?
(Select all that apply.) The graph of f has a hole. .The graph of fhas a jump. i The graph of f has a vertical asymptote. IX None of these. \/ 2) From the graph of f, state the numbers at which f is discontinuous and
determine whether f is continuous from the right, or from the left, or neither. _'i (smallest value) \/ continuous from the right continuous from the left X neither \/
x=" “1 / continuous from the right x continuous from the left / neither X = \/
y continuous from the right continuous from the left Student Name: y continuous from the right 'v ' continuous from the left neﬂher
3) From the graph of g, state the intervals on which 9 is continuous. (Select all
that apply.) A ’ (w. 4] ' (m. 4) ' [+21
[4.2) /
[221
(2.2)
[2.41
[2.4)
[4.61
(4.6) \/
[6.81
(6.8).
[8.m)
(8.00) TYWWT‘X “iii jj‘ﬂ 4) If f and g are continuous functions with f(3) = 4 and the following limit, ﬁnd
9(3) Student Name: 111713.: lfiJ'} — yin)! : T ‘27 L’l — ark‘3 3 7 \/ / .
q \/ ' 19‘ {'6 *3;37):7\/
5) Locate the discontinuities of ét/he function. (3 i i q \/
u ,x i = V {g v 1+ (3 .  0 MW
J 7+ r" ’ k ‘ I I! — I .
IO— / , )4 o if; sz) =37 wae3<mci —) é Wuhémc‘
6) Use continuity to evaluate the limit _ 1 v i a .w lim : ~:—, _E 1 \/ (i Q.) Lm :gﬂvbv
72 t1 3H" "t r " f 7L.—
_  .«k\ Kid/7"?“ I L .A ‘
57 I I L; I I‘, Lorduwaug. Oat __
7) Use contrnurty to evaluate the limit.  I!” fill? (Shaw) J19 acn‘hmwsm (—00.00) =>st" :un'iimi “u 0 (bume
i #60 3111(X—i'5nnx) :3 : km (ii‘t H11? '5 irih‘ﬁm; 8) Find the numbers at which f is discontinuous and determine whﬁher {is——T£m:3'_'—"c
a = _ I L
air1:” Modal grunt—x fix) {:35 ifJ' 3'2 H ‘ V ‘ '
*1: i mnirnuouz. at x: O?‘
1;.“ to): 8—0: x, Um _£(x) =i+o€®, grog
x~> 0’r K40 (I continuous from the right :3 3‘ is um’rinuoua “Hm i=3}: D _
‘7‘ continuous from the left \/.*.13 » mn‘hmuu; ed x: 82 " neither ‘m,r tax AIS923(5)? L$mgpﬂl):g—X©, 35%):@ 9) Find the numbers at which f is disconti‘nﬁgus and determine whéther f is.\ .=) x5 maﬁnuouy> continuous from the right, or from the left, or neither.
.r' + {3 if .r' ::I U _ a
rm = w 11' n 5. ..~ J $0 hf 7.! ilﬂr 7:: I X: O (smallervalue) \/ at X=Q ﬂ . _ 4% lg Wd‘Moug a} x = Q 1)
F continuous :rom t:e {rim \/ \m (X) __, L0: Lm 2 014, = Q, ) gm) I! contlnuous romt e e x_) 0+ K 4 OF
' neither I ‘ ‘ I ‘
é l3 digcon+trwcug (ﬁt 0 (I a) LVN. clot?) x=.[ \ (Iargervalue)\/ mt and). Hnwwar, i jg mnﬁxnjﬁig [A He ha H 64f o . continuous from the right i continuous from the left V 4% lg Con+\Y\uCd3 cht x : i (Z . ' ' _ , m  ,1 , $2th Ms Eigeer : , i(ﬂ):@)) HA) _ i r o‘iEamﬁm a} _i_ _! (7r)c\o_c1 rm“ exist a wax/or, is
éNi'ENIOUS kit Lil‘s \ Kati] _ Student Name: r .
neﬂher a 1d)\For what value of the constant c is the function f continuous on m, m)? ~
H H : { rag3 + ;$.r if.r <13 Alﬂ is mﬁ]mw3 on (_ 00) 5 U ( 5i+ob)
‘ ' ' .r‘ W rar if .t' 2 £1 M T X z 3 wt _ To _‘ 90“ *wuvi & , ‘ I
c= :lob Liijx) : Lt.qu ugh) :__f(5) => (:6 + f) : 21_c.3> = 214.5 , X432 7“’3+ = C3c+9 : Q}3c =5ﬂzczlg’
11)) Assume that f(1) = 5 and f(3) = 5. Does there havet be a value of x, Between 1 and 3, such that f(x) = 0? Picacabs} "on: ln+ermycknﬂﬁ Vain (TEMM, i
L1G}; “loo L2 Can"\m»0M cm E M «(hr—k1:
86:8 ates 4L “me if >< 19mm 4. mi 5) .
(INCL “Hat : O . 8c: WE donut L'xhgu‘a ‘IIDOQJT wn'x’lwéha (5? LE) WC.
(la/arm": 8&3, admit walk“. X. ...
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.
 Fall '08
 Noohi
 Calculus

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