math161 s07 midterm1

# math161 s07 midterm1 - Math 161 Midterm 1 Name-l_y.U Date...

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Unformatted text preview: Math 161 Midterm 1 Name: -l: . _ _y..U Date: February 2, 2007 Instructor: Dr. Paul Choboter Time limit: 50 minutes Read all questions carefully, and Show all your work neatly. Calculators, books and notes are not permitted. Good luck! Question Score Points possible 1. In this question, let f(3:) = 952 + 3:1: — 4, and let g(m) = 5x V 39 — 2' (5 pts) (6.) Simplify the expression f(a: + h) — f = we“ Jr Sec-3% *4 — @14ch "4) : t _;'l.,-'% XL 921% : Zx‘ﬂ +h7‘ + 3‘0 f (5 pts) (b) Find (fog)(:c). Do not simplify. \/' (C 43 XX.) 3; 2 1— % (:égﬁ —4 ‘3 7:2 xvi 2. Suppose that the population of groundhogs1 in a certain park is given by N (t) = 160 x 2“, where t is measured in years, and t z 0 represents right now. (3 pts) (a) What was the population 2 years ago? (State your answer explicitly in the form of a single real number.) Na) :\l00x7_” : \loO x—Z‘; 3 :ugox—L w w.) : 40 Straw-MT; . . J (3 pts) (b) Write the groundhog population in the form N (t) = 160 x e“ for some expression a. _ 0. C? F “00 K 6’ [giléfig_w I a ‘ Man“... a \bO ‘ e a l a 2 12mm) ﬁnllbm a so a e e—W-mm—m J‘L _ 0mg“) _ or bum) dam Luge) : Oi (4 pts) (c) At what time t will there be 1000 groundhogs? (Leave your answer as an expression involving terms such as 1n(160). It is necessary to isolate t, but not necessary to simplify the expression.) t i_ J #mem.__,...r,mm.--“Mummw \Om —... \em 2 “19000 4%! ll 3999 : it t \ogz U00 t .m,...W_M-—-w—----—-»Mm-w— ____ w wee? = W51 logmoo —\09 V00 : twos ’2. HE]le ‘lg Ugo: loop, 1Happy Groundhog Day. \ﬂ’FCll 03 3. Plot the followin functions. g W1thth {4 pts) (a) Plot f (cc) = 2sin(cr) and g(m) = —cos(3:) on the same set of axes. Clearly label which curve is f (2:), and which one is (4 pts) (b) Plot = ﬂ and 9(59) = Va: + -— 2 on the same set of axes. State how you get the graph of g($;from the graph of f($). gtrﬁ I: We 1; moved 1+ — 7 m0 dcmm the +0??? becauee 09 W‘ﬁ “— and one WW \eg-l- on We Xv QXlS becauee 0% WW- ” n undﬂz «he 0“" Mn L3 addﬁd ‘bo *tWCK. (2 pts) (0) Clearly label the following numbers on the logarithmic-scale number line: 0.03, 0.2, 40, 700. \/ V' t/ l/ 10 (5 pts) 4. (a) Let y = 255—3/2. Use a logarithmic transformation to ﬁnd a linear relationship between logy and either logs: or I. Determine whether a log-10g or a log-linear plot should be used to graph the resulting linear relationship. —.3 u—- 2. V 34* 1 “er mew") v}. 2 5. Evaluate each limit, if it exists, or state that it does not exist. Show your work. (2 pts) (a) lim 32—.— wmwm ka (4+h14+h\ —\ b 5 $+5$2+2$—15 (4+h)2 — 16 h—ao an :' has h \0 (Wm) _ ,_-— (5 pts) ((1) Let ﬂax) be the function o % Jam - _ _ 3/ h “7% (x @3 2 E: 3 m 3+0 ._.._ : m WWW“ fr“ WT ﬁi ﬁw MD if m < —2 if — 2 S a: < 1 ’1‘ I if a: > 1 \ A L '37. ‘" ’5 '5 909$ hU’fENSF (—1314 2 1H 3 ’2. ...
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