Practice Midterm I - 5

# Practice Midterm I - 5 - 07:39 IFAX...

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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 / . I-D—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 /_ x-rS‘ 10. x241": \$15 / w,— ﬁmlﬂ- KM x( - j: X34 xL-Bx-‘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 lag-41w W wag/<5) b) [4 marks] Using the epsilon-delta 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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