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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 (nonzero) jerk? ...
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 Spring '07
 Sullivan
 Derivative, Velocity, Limit, Limit of a function, Blair D. Sullivan

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