McCartin_Test_3_Fall_2002

McCartin_Test_3_Fall_2002 - MATH 101 TEST#3 Professor Brian...

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Unformatted text preview: MATH 101 TEST #3 Professor Brian J. McCortz'n December 13, 2002* 1. (20 pts.) Boyle’s Law states that when a gas is compressed at a con— stant temperature, the pressure P and the volume V satisfy the equa" tion PV = C, Where C is a constant, Suppose that at a certain instant the volume is 600 cm3, the pressure is 180 kPo, and the pressure is increasing at a rate of 30 icPa/m'in. At what rate is the volume de- creasing at this instant? 2. (10 pts.) Find the linearization L(:I:) of ﬁx) I oils at a z '3. 3. (10 pts.) Find the differential dy of y = coss: and evaluate rig for :c = air/6,0311: = 0.05. 4, (20 pts.) Find the points on the hyperbola y2 "11:2 = 25 that are closest to the point (5, O). 5. (10 pts.) Using the Mean Value Theorem, show that x/1—2\$<1w\$if0<\$<1/2. 6. (15 pts.) Using l’Hopital‘s Rule, ﬁnd , e3 — 1 11m _ . :HU Sins 7. (15 pts.) For ﬂat) : 1:2an 0 Find the intervals on which f is increasing or decreasing. c Find the local maximum and minimum values of f. c Find the intervals of concsjvit}r and the inﬂection points. *WARNING: SHOW ALL WORK! E £55): M639“ 15H ”T€§+*\$ giakuétmws h EAL 9 {Gt} “' “4* "‘ - 5-1:? ' ' ?m§ H5 Cow/+M ‘r‘oLKKlOO'D. =. m . . _ . . _._. __...._. . .. ..__.._... ...
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