{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

winter_2010_1

# winter_2010_1 - MCV4U CALCULUS AND VECTORS Date TEST...

This preview shows pages 1–4. 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 is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MCV4U, CALCULUS AND VECTORS Date January 25, 2010 TEST Chapter 1 LIMITS Teacher: Teodoru Gugoiu Name 1. The function f is deﬁned by the graph represented in the right figure. Find: [KIU 3 marks] a) xﬂtﬂjtx) = L b) lim f(x) :0 .7r——>—4+ 6) lim f(x) DRE. x44 d) lim f(x) == ‘r xm>0 e) limf(x) 10° x46 f) lim f (x) '—'- '2. x—y—z 2. Consider the function defined by the graph at Question #1, {C 4 marks] Analyze the continuity of this function (continuous or discontinuous) and the type of discontinuity (removabte, jump or infinite discontinuity) at the following numbers. Justify your answer (explain why). a)atx=—4 «3'? ‘tb éi\$wm4€huou\$ and if:— UVL ¥v.c>¢) == '1, #‘r Lt“. 4L!) a; 63 RP“? Algmuﬁhbt‘ﬁ) l u-‘J—HJ- , #4) “‘tf b)atx=0 «h 5 t K O {I * , . " q -: ‘ ‘ f . -°- 4:. “5’ 3‘5““ WW t tub om: (vewqulo\€ d‘s‘w“ m” ‘5) MW L36): L‘" 1’3“- — )L—‘Do c)atx=—2 Kim 3r“) = ‘1— ': {“23 )L—>-'l , Q— ‘5 mu‘uhu ouSq‘t Y =-‘—'2. a. UUL £L.,(') '2 0‘9 L tu‘timi‘tﬁ, obscouﬂuu Hg) 3 f tx)_- gm _ [K/U 2 marks} 3. Given lim f (x) =3 and ling g(x) = —6, use the limits properties to find Iim x-—>0 “,0 2g(x) L‘ '5 qﬁat) TESL“) likaf" 1”)" at“) 1 1) (Etta; PK") ”"8113 -: ‘luL... -.-= 7) -; M Q {as 1°35“) hm [2 ﬁnd] '2.. QjUL 0&0 ’(‘Do that = bww :_ BMW ﬂ 1-}: '2. C— 6) "m, #- r+ o Q‘s: -— r.b/l-l- Page1of4 4. Find each limit. [KIU 12 marks} '3 [1]a)1imx *3 8 _. LIZ—3.” :3: —+ x—ﬂ x- 2 "’ "" 2 —- =, n. --—— '9 H41: +2xA8 I K...>__\+ Cgﬂz) cw 1"‘5-4'." ¥fl '"Q'"? E [2]c) lim 4 ‘6 Lu. CfW/ﬁ CH?) C" “+7 Um. 0H2) CRT-H) 4-68) 1542 _. 3 =—' x s pun, wcilﬂﬂmwzm2¥*ﬂ p); 17—52.th- \ _. - (\l‘ tr ‘r [21mm ”‘16 “Um.” ‘6 ,W'H' =\A~M_ (Msth-k xalﬁJE— 4 ﬁ—‘J‘Q w_|+ W 41"? ﬁ.-§\Q X _ {é {’b‘a l .. “TE-Ur l x 7‘5 [21e) 1m x 3 2:2. = 7’ “HUT-3| ‘wab‘ .--\ 3 x 45 . x—3 .9. x—‘a but" "Cc—31“ ?‘ Kim. K =4 .1 ML- \x 3‘ ONE- K»; alt-var “("51 x» 5 '" 5. Analyse the continuity of the foilowing function. Graph the function. ' [A 4 marks] x2—2x+1 , x30 ‘ ﬁx): 1 , 0<x<4 X J; x24 “1‘ " = ° w 1 _ ’_ \ 5‘ L’- wa X4!) =\J‘~\M Li‘ ’2’“) " L5; Um. Kim) ”(Li-tr X‘JJ’Q. K96- K.) Lt" y. (L. x a: |+ :1" L. *‘| Kim Q“) 5L4“ . K a: Um ho :Um — K :1 #va 5 1-)0'1' ,L-w'au'k at r, ‘t 1» §C°U=omﬂlﬂﬁf|51 L—‘I‘bk -~'1- =9“ “*0 .. 939“”? obsmﬂuuﬂ‘ﬂ ~ JUMUWS J #91:: ‘Q‘ ‘5 w“ '0 Page 2 of 4 6. Consider the following position function: 50) = r2 —r3 [A 6 marks] [1] a) Find the average velocity over the time interval [1,2] ”Lt '—'-‘-\ > St = 5C0 ‘5 \l’\% ‘1'" 0 sq. 3 :sm: lvz3=irrﬁ=4 t1 '3 7/ 2‘ . kv=ﬂLkWIS MSW-s =—‘-*°7-:_LL—_—_._Lt.uils .. ’c 1 '" ‘l t L ...— ‘ ‘ [3} b) Find the instantaneous velocity at the generic moment t: a. Show your work. '5: SCOK-t‘n = Cq‘t'ﬁl" (‘Hm n, ’ \$Lq-UO “Sta? {magi-- Cot +u33—q1-tq Qo-ka—QL-t City-— (0601’ \n K k = in u — 'L 1 : )(tu-t m3 +t ”WE“ t «(quit (“9313: Lm+k_f_q1+qtqtt0 +(‘i't‘01 \I‘ZUU-Ln [204M +Q?éq.Cq-tk)—Cat+h)a _._ LOU- 'bqq- “‘9'“ 9. . io— glee-30.. [1] c) Use the formula you get at part b) to ﬁnd the velocity at 1: —2s. '1. \r’ (#2:) == LL-Z) "3 (2‘2) " "t—\L==--\ Q :0 VC’13Eh\GUI\$ [1] d) Find the moments when the particle is at rest. '1. .— : 0‘1 Q‘s—- v‘Ua-m g) lq_3QL= o :7 qgmﬂgQ—Lo w) 0k 0 .3 .t. hair-tide 3qu (9313' it {.595 O‘L- tr 2:1; \$ 7. Find the equation of the tangent line to the graph of y = f(x) = 4 at the point P(i,2). Show your work. x+l U ﬂ Li. __ [A4marks] m 7E: W0: ‘m. HM ti 9' lew». Lt __ lthM3 ‘H'o ‘“ u». (Hi0 in. :quiuw no. ___‘ .M=.—\ M.» ,JMHVO wk, Lam ” " virtue—i064) => “3=—-)<-i-it2— 31.413 8. Determine the instantaneous rate of change in the surface area of a spherical balloon (as it is inflated) with respect to it radius, at the point in time when the radius reaches 20cm. [A 4 marks] - . _ 2 ._ Hint. 24—47:? [3410110 ____ RCZo) Lg; (go-tuyq-ﬂ Lt“ (loft: \Lc:U\M- ”—7: = Kim-- ~————-————_\J\LL.M Adz-9° A “.57, Vi iii->0 M @ﬁuf— may“ Lt” OJ K Lu -t\/L* to) _ 3 ti UL— M '— '" u—: o in was W \A~‘> o :_ \LQ, = \Gro'Ti w». Page 3 of 4 1 9. Use technoiogy (a scientific catcuiator) to estimate the slope of the tangent line to the curve y=x+ 1 at the x_ point P(2_,3) by using h] = 0.], h2 =0.01, and h3 =0.001. Show your work. [A 4 marks] in. -i— 3 it ) 1‘ " if; ’ (b I}. 0.1 "’ L ' __ . uur: -—-—-————--——-Ldr = w‘ 1.20.6"ng G-i Oil ‘ —3 i (Lemon -— £tﬂ 9- ‘°‘ "' ..._.———-—-—\]________ uh, as. o M =‘— 9-4“ “ 0.5 o ”b"? ' mm '2': __._...._________ —; ' \I .. .— UU; 0‘ Dbl '2...DD\ I r: 0-5 00.51 0- 0 0| ,o. \M Cr. 0. '5 10. Consider the piecewise defined function below. Find the values of the constants a, and in such that the function y = f(x) to be continuous at any number. Show your work. [A 4 marks} 4): , xSl * f(x)= ax+b ,®<x<2 ~5- , 22 x x Q) qué® “'17 At it ﬁt it '2. 8.09% L. La- UN “40: L" L‘Un in? lq'tb {Lat-00:40 ,,.. (.) pvt" tch-n," W ‘L 1.“ UN 9'1!) TSQ—k‘o 15““. got"): *5—{7-3 1:"0 CL. ‘5 V3)” tut->1} 5—5.. is“); \$00 = H“ 9-in =‘Lo © :1 :2: :0 H =1»be ® 0 Q—DL'UO—J— ‘0 = ‘ p..— QUd‘D:\e‘ " Q'i‘acoub'kuousaﬁ (1‘43 kuuﬁer L‘Q‘ 0w»- W from: -—\Lsx-tk83 \‘V‘L 1 1 11.00mputetheiimit um" ‘5 . [TiPSSmarks] “Kala/\$.71 \ 1. J." —‘-—t—-‘- 3-1—7 X x’}. . it“ Y~ . " “=- ‘W' ., “I - —--———---" “1 W—-——*T":' "hk'r'TiT-t’") ’H‘ v.4 £‘t‘xﬁi ”‘83? "XY’W’Q H‘ N?" t W 3 '5 3 _. t—- . _ - =, \j X 1) _‘___.Z<.————-"" -=-. .L— ‘w __..._.g_——~—-—- 3 hp“; 3“ X ﬁ \IL. \ \ “b ‘5 ___\ IL “’7” U" ,(g‘ 7‘* TEK ("2H {X '5 H; \JcU-tu") t _ _.. ow». th 3C “auto-W a. u—at “.4 “v" Page 4 of 4 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

winter_2010_1 - MCV4U CALCULUS AND VECTORS Date TEST...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online