MidTerm F06

MidTerm F06 - MATIOI Fall 2006 — Blair D Sullivan ‘ 1...

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Unformatted text preview: MATIOI - Fall 2006 — Blair D. Sullivan ‘- ' 1 Midterm Examination 1. Name: Instructions: You will have ninety (90) minutes to complete this exam. Calculators, notes, and collaboration are not allowed. Please show your work, and write legibly - no credit will be given fonillegible work. Note that the more steps you show, the better your chances at partial credit if you make a. mistake: Place 'a box around your final answer(s) for each question: When time is up, please write the honor code and sign your name on this cover page. Good luck! MATIOI - Fall 2006 — Blair D. Sullivan Question 1. (10 points) Given the functions f($) = 5 + eSc and g(a:) = 3/13, (a)Findh=gof. I r (b) What are the domain and the range of h? (c) Is 9(33) even, odd, or neither? MATIOI - Fall 2006 —- Blair D. "Sullivan Question 2. (10 points) (a) Express the following in terms of In 2, 1n 3, and In 5: ln(.12) + 111(150) . 10g2(9) (b) Find a simpler expression for: eln 5:12—an ,MATIOI - Fall 2006 — Blair D. Sullivan '7 ‘ 4 Question 3. (10 points) Find the limit below (hint: use the sandwich theorem): lim \f2—9(3 — cos(1/9)) 3—4] MATIUI - Fafl 2006 — Blair D. Suwvan ' 5 Question 4. (10 points“) Given the following limit, and e a: 1, find an appropriate 6 satisfying the definition of a limit: limx/7—a:=2 I—‘3 MATI 01 - Fail 2006 — Blair D. Sullivan 6 Question 5. (10 points) Find the tangent to the curve f (3:) = 5:1:2 - 7 at the point a: = 3 using the limit definition for the Slope of a tangent line. MATlOl — F311 2006 — Biair D. Sullivan Question 6. (10 points) State the definition of a, left—handed limit, and find. rm 3:2 — 16 3—.4- [:3 — 4| MATIOI - Fall 2006 — Blair D. Sullivan 8 Question 7. (10 points) State and use the three step continuity test to find where the following function is continuous: 2552—2 —1$3:<0 3:1: 0<sc<1 0 3:=1 —:c+4 1<$<4 m) = MATIOI - Fall 2005 — Bun D.'Su111'van ' 9 Question 8. (10 points) Find all asymptotes of the function {8m2—5z+6 a: Z 0 ' 232—1 —e‘” —5 a: < 0 f(:v) = You should ShOW the calculations that justify your answers. Sketch the graph of the function using this information. o MATIOI - FaII 2006 — Blair D. swim ‘ 10 Question 9. (10 points) Take the following‘derivatives (you may use all the ' derivative rules from section 3.2): (a) f(:r:) = “2+3”, find f’(:v) ‘ (b) 905) = —2t_1 + 4t2 + 35*, find gig and 5529. MATI 01 - Fall 2006 — Blair D. Sullivan 11 Question 103. (10 points) Suppose a ladybug is crawling along the windowsill with position given by 5(t) i 2132 — 315 + 1 where distance is measured in inches from the left hand side of the window, and time is in seconds. Find the following: (a) The average velocity over the first 4 seconds. (b) The velocity and acceleration at time t = 2. (c) Does the ladybug ever stop moving (have zero velocity)? If so, when? (d) Does the ladybug ever experience (non-zero) jerk? ...
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MidTerm F06 - MATIOI Fall 2006 — Blair D Sullivan ‘ 1...

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