Ernst_Test_3_Spring_2007

# Ernst_Test_3_Spring_2007 - TEST#3 g e NAME MATH 101 7 9 re...

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Unformatted text preview: TEST #3 g e. NAME MATH 101 7 9 re JUNE 3, 2007 ' l. (6 pts) Ohm’s law for electrical circuits like the one in the ﬁgure below states that V= IR, where Vis the voltage, I is the cunent in amperes, and R is the resistance in ohms. Suppose that the resistance R is held constant. Find the rate of change of voltage with respect to the current. ( dV/d! ) V .- } ”'2’:- 5" r, .. I}: f .1- {I | i _ z? i R ' 'Jl'J-J i o“! "T:- : ll {fl 2. (9 pts) A spherical balloon is being inﬂated at a rate of 2 £113 lsec . At what rate is the diameter of the balloon changing when the diameter is 8 in ? (V olume of a sphere is; V = i 7, r3) ,.. f' ( : (bf 3 A .f-r-I -' D1 (A {i t. a; [,I ‘/F J 3 “I; I J P1— i1 3 YT, q “— I r "1' _J ? (ff; as r_'_ 3 - L V: _: fl: J “z ’ }_ J ("J H Li ‘ ’ ( 3:: ‘7..- [I ‘- LI ,2 3 1' .r "ff I. r1; A j I a“; I f ’l' “f Iii-231's c 9““: "—‘H-ukl. ' 3. (8 pts) A particle moves in a horizontal line according to the position function, s(t) = :2 —6t +12 (cm). a. When is the particle at rest? (Find the velocity.) v ,, gt- (a we: 2-(‘5— ' ‘53 973.- f‘ﬁrﬁ.‘ J‘Nﬁn f, '—- 3 b_ State the intervals where the particle moves to the right if _ Y in .. 5 31 =Hﬁ.€ (":5 Li— C‘Ji‘hlr- t >3 rt -_ VII I) 'Jp- 1’. 'v- ‘ 4. (8 pts.) Find the linearization of the function. f(x)=ln(x+2) at a=-1 ‘ I "1‘ i 2, / ' " i ’ ‘ yzx-l'i ’1; if”: 4' iri'i/ - ><-+ J. 5. (7 pts‘.) Find the critical value(s), yum I xﬁw—u‘a- '24} 1 O ‘f '3 3:. I; f. '. . :l ﬂ . If; ‘1': #3, 3 liﬁbi A: _ 72>H— _ '2" f” :7” CN" ’5 j; am . f(x)=2x3-—3x2—12x+5 on [0,3] {9(y—2 I; 4i) 7. (22) Given the ﬁmction, f(x) = 2x3 — 6x + 3 . a. Find the intervals on which f (x) is increasing and decreasing and ﬁnd the relative extrema. My, _ ,_2,/ ,. -_'_ . 'Ljr‘ p «ii-('1‘) ‘3 7 Wm“ b. Find the intervals of concavity and ﬁnd the inﬂection point(s). rt! :5 Z" - '3' F" 0 t f /\ 1 u 8. (16 pts.) Find the ﬁrst derivative using logarithmic diﬁ‘erentiation. 3x 4 e (x. ) a. = y 08—8) ‘3? ’ LI i1” {7— th C. "y : .—...,_.—--’-'-'-_Fl_- .2‘. i (L 41;- / ' ; b. y=xﬁ # Q,r’ *M’ 9. (15 pts) Evaluate the limits. Support ALL conclusiOns. a.1im 1—50 c.1im x+l cosxul 0 x (2 e3: _eﬁ £3 ,_ L's x—l ”ff ” 1:3 +6172 +11x+6_ x3+l \I\ a. 7' Y _, O ...
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