This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: (16) MA 165 EXAM 2 (makeﬁup) Fall 2009 Page 1/4
NAME GRQWWG reg“?
‘Page 1 / 16 ‘
STUDENT ID I Page 2 /30 l
P 3 26 ‘
RECITATION INSTRUCTOR age /
Page 4 / 28 ‘
RECITATION TIME TOTAL /100 I DIRECTIONS 1. Write your name, 10~digit PUID, recitation instructor’s name and recitation time in
the space provided above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one.
Write your answers in the boxes provided. 4. You must show sufﬁcient work to justify all answers unless otherwise stated in the
problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin.
6. No books, notes, calculators or any electronic devices may be used on this exam. 9° 1. Find the derivatives of the following functions. (It is not necessary to simplify). NFC
(a) 2 e39” cos(4a:) (C) y = tank”) (d) y = 1D(Sin(€‘”)) MA 165 EXAM 2 (makeeup) Fall 2009 Name Page 2 /4 <6) 2. If Fe) 2 f gm), ﬁnd M) if f(1) = 3, 9(1) = 2, f’(1)= 5, m = 6, l
f’(2) = 4, m = 7. V E if {62‘s} 3: gfgﬁésfxﬂ (3/00 @ x /
F’i’i) e Wﬁ’i}? 3:747 (29 C3397 ’ 7:: 442—324» __24“ 9 . 1n an equationo t etangent me tot ecurvea: +y =3y+8att epomt —2, .
3 F' d ' f h l' h 2 h ' 4
%X+Z‘%é§%:3%@ an m 33‘
«:2ng (it! {i «: aﬁgﬁ
4&0 F? “2;. 26%) mi X
dim C7274") “3mg w :3“ ‘ ‘ 4 F 5%.
, w 2.
d3? 5%.; : 3,42%01‘4”) L5 ‘“ (M ” lil
‘ a '* (9:) I
(9) 4. Find the exact value of N ?Q l
l? l
(a) cos”1<——%§1>t::kéi ijerg Os‘iérf 53; l @ i
,6 “SIT G . l
Vang T W
(b) tan—1(—\/§) 3; Li $7.5 tonne; t” 3}"2'< ‘é<'§l "[1: ®
” 3
(c) sin<2sin—1<—;—}1 f%\n2~le?%ma:wé= 2' lav—‘37:? ‘
Lei: jzsi: (a) Sign“; :29 7, COS :{Laa‘w 21— 1— #:3— ,
‘9 ‘3 + r
cos “E E “'3 ©
‘3 2 (6) 5. Find the differential dy of each function:
(a) y : msec(3x) ohjctjx emcfh) Eanéx)f3 .3. eeeﬁaﬂix
—1 Ft, fair misshme Add: dy 2E eecgﬁxﬁ Tomﬁbﬁfl‘)‘ +$eir©x2dx @ a1 Ylozr méﬁilnélas‘gi dyzeﬂwi‘ wgtdﬁa ‘ @
aw MA 165 EXAM 2 (make—up) Fall 2009 Name Page 3/4 (12) 6. Find the derivatives of the following functions. (It is not necessary to simplify).
(a) y : tan“1(w3 + 1)
N W
1 , 2
M a ’3:
(x3 $122+ 1
(b) = sin"1 ﬂ
ﬁ—G—Lﬂ’ i ’X
R:
9};
\i
“ximx 22%
PX (8) 7. Use a linear approximation to estimate \/99.5 £00 Q‘i K09 i“ Elm) (pa!) I PLOV 7: Fiﬁ/(UV CL I g» / ﬂy is
{00 :ﬁ@ @100) f(1,00)::lO/‘ at (gem } f (mo .g 20 W 9573.0 'V‘é’a (X'10C5> {.o‘w‘ Xﬁmjr :30,
\l " O l “3: ’ — 4W2? ﬂowing
m {ii mg“ 05”" m “Q79 was (6) 8. If a ball is thrown vertically upward With a velocity of 80 ftsec, then its height after
t seconds is 3 : 8015 — 16t2. Find the acceleration ‘of the ball when it reaches its
maximum height. (311: “431 Macy 31; 36?: set? El #5 MA 165 EXAM 2 (make—up) Fall 2009 Name Page 4/4 (14) 9. A kite 100 ft above the ground is being blown away from a person lying on the ground and holding its string. The kite moves parallel to the ground at a constant height and
in a ﬁxed direction, at the rate of 10 ft/ sec. At what rate must the string be let out
when the length of the string that is already let out is 200 ft? i1 , 2 : WEE; ,f 40 3M" gag: y 100
"" [VVLCi 4w lmaif? O I
all; U I”
“ 2
kg; X2+ gm}
2% as a; g aha @
(if 3%; :— 23. “a calf
\Nlum 2260' 3‘ iEQQg‘Wweg =11” 1430005? Mason 2:.
W7“ :2 V“ a, we?
«a; . m g 5% git/save:
Gig: 200 @ era iii/gig; 10. A spotlight on the ground shines on a wall 100 ft away. A man 6 ft tall starts at the
spotlight and walks directly towards tgewall at 5 ft / sec. How fast is the length of his
shadow on the wall decreasing when he is 50 ft from the wall? (Let :1: be the distance
of the man from the spotlight and let y be the length of his shadow on the wall).
% “Ki d}:
if Final» ﬁg WW WtSQf‘t
I»; « MUM i WNW “6‘ "if ‘
far—w mo m 7 Tag .., x
m we
‘3'“ «a i
at « goo is:
0:1: V “X?” 53% ® I
Whita #353: ﬂmﬂg00.§=wgiz/Mﬁ
“m““"“‘”“”“*”‘“’ (Lg: —— 2500 Q The. léi’hegiih a}; Msslnaaiew '9:
ciut‘eaisémg, aittemti ...
View
Full Document
 Fall '08
 Bens
 Calculus, Geometry

Click to edit the document details