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Unformatted text preview: 05/20/2004 07:39 IFAX [email protected] —> Connie Ooster I001/008 McMaster University
Mathematics 1A3l1N3E Prof: C Brady
Duration of examination: 75 minutes «May 17, 2004 Name:
Student Number: Tutorial # or Instructor: —_——_—_—_——————————— This examination is 9 pages.
Part A is simply ﬁll in the blank. One mark for each answer. Part B is complete answer questions. For full marks show all your work with clear
and concise explanations. Be sure to have proper mathematical form. N0 CALCULATORS are allowed. There is a blank page at the back for any rough work. 05/20/2004 07:39 IFAX [email protected] —> Connie Ooster I002/008 4————— 'I
Math1A311N3E Test 1 Name: 50:! Page 2 of 9 Student #: PART A: Fill in the Blanks. Each blank is worth 1 mark. 10/,E% 6 ’9:
G2 3. Ifthe function, f; is continuous at a, then lim f (x) = i (a 1 .
4. The Domain of f (x) = arctanx is i 2 . 5. Let f(x)=a’ where 0<a<1. Then limf(x)= [‘13 / . ID—n 65
. . 3 / j 9:34 8=%ZZ
6. Snnphfy f(x) = log2 24—log23 = . ‘32 5 J;
7. The “Horizontal Line Test” checks to see if a function is Z 7%“ FL / CY ./ 8. Ifa function, f; is odd then "X : h 9. limLxJ = 9L /_ xrS‘ 10. x241": $15 /
w,— ﬁmlﬂ KM x(  j: X34 xLBx‘f X's?” (@(KHV 5" 05/20/2004 07:39 IFAX scanner©mail.math.mcmaster.ca —> Connie Ooster MS“ Math1A3/1N3E Test 1 Name:
Page 3 of 9 Student : I003/008 PART B: Full solutions. Be sure to show all your work in concise
mathematical form for full marks. 1. [10 marks] Evaluate the following Emir“
7
=0Z’ow m0)?! M % 5/516? Arﬁw‘Zd"
® a) "*3 x—3 X93 (’93 05/20/2004 07:39 IFAX [email protected] —> Connie Oostel" I004/008 Math1A3l1N3E Test 1 Name:
Page 4 of 9 Student #: 2.21) [3 marks] Using epsilon and delta, state the precise deﬁnition of a limit.
In other words complete the following statement. 1imf(x) =L means ﬂx % E>OWMDMQL é>0:‘1:4/
010m «5795“ 1ch— G lag41w W wag/<5) b) [4 marks] Using the epsilondelta deﬁnition of a limit prove: . mam—3:9 05/20/2004 07:40 IFAX [email protected] —> Connie Oostel" I005/008 4/ ’1 
MathlA3/1N3E Test 1 Name: Page 5 of 9 Student #: 3. [4 marks] Solve the following equation for 0 S x s 27‘ 3cot2x=l ’3: ”tr—it “WWI 3”?”ij 'P' X: é/g‘QF/B/ 0%) 57% V/‘// 4. [4 marks] Solve the following equation: 1n(5—2x)=
, l —3
5" ng" 6/3 /
'o’zx' 25,5. /
>< iii—J" 5) /
 2 63 05/20/2004 07:40 IFAX scanner©mail.math.mcmaster.ca Math1A3/1N3E Test 1 Name:
Page 6 of 9 ' Student #: 5. [5 marks] Prove the following identity: tanlx —sin2x=tan2xy
‘7— . CODEX "’ Szn X”
' %(/' I 2x) ("I
07226
?
': SiﬂfZK—FT; X 0"f_ "* [(28A. )C (”x /< 6.  [4 marks] Find the inverse function of: 9 Connie Ooster I006/008 05/20/2004 07:40 IFAX scanner©mail.math.mcmaster.ca —> Connie Ooster I007/008 0/ A 5
Math1A3/1N3E Test 1 Name:
Page 7 of 9 Student #:
8. [8 marks] Find the equation of the line tangent to
x —1
f (x) =
x — 2 at the point (3 , 2). k
2 A 52% ”'2 M ,1.
ﬂat) l+h l+/1 A /
: (ZAWCZ‘M'Q’52‘ /
A290 [+A A MathlA3l1N3E Test 1 Name:
Page 8 of 9 Student #: 9. @ralrks] Let f (x) = 1n(x) and g(x) = x2 16, a) State the domain and range of f and g. b)Findfogandgf.: c) State the domain and range of fog and go f. a) D¥=(O,w> /:D3:/’12/
2! T2 / £5rE/éatﬁ/ E) G WOO ((309): A(X~/é)‘/
(fﬂﬁﬁgwﬂf («Z/M)”/é / ...
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 Fall '09
 Dr.Lozinski
 Calculus

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