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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'JJ i
o“!
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{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 .frI ' 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 Iii231's c 9““: "—‘Hukl. ' 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 ’ ‘ yzxl'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;
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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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 Spring '08
 Walker
 Math

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