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 DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Exam 2 Math 4080 Name Fall 2009 TA Discussion Time: TTH You must Show sufﬁcient work in order to receive full credit for a problem. Do your
work on the paper provided. Write your name on this sheet and turn it in with your
work. Please write legibly and label the problems clearly. Circle your answers when
appropriate. No calculators allowed. 1. (14 points) Let f(a:) = 2 sin3 :5 — 3sin x, 0 g x 3 7r. Find the absolute maximum
and the absolute minimum of f. 2. (14 points) Describe the concavity of the function f = ~33— and ﬁnd the (1 + 231:)2
points of inﬂection (if any exist). 3. (14 points) Find all horizontal asymptotes of the piecewise function
v £62 + 2a: — 3 <—3
517—1 ’m‘ f(£v) = sin :13 , x > —3
a:
4. (14 points) Water is pouring into a cone Whose height is equal to the diameter of the base. If the height (measured in feet) of the water in the cone at time 15 (measured
1 1 + t2’
at the moment the height of water in the cone is % foot. (Volume of a cone of height h and radius of base 7‘ is V = §7rr2h.) in minutes) is given by h(t) = 1 — ﬁnd the rate at which water is pouring in 5. (14 points) You have 100 square centimeters of material from which to construct
a box with no top, having a base that is twice as long as it is wide. Assuming that
there is no waste in the construction, ﬁnd the dimensions of the box of largest volume
you could make. (The volume of a box is the product of its length, width, and height.) 6. (14 points) Find a function f satisfying f”(a:) = sina: — «5+ 1, f’(0) = 3, and
M) = 1. 7. (a) (8 points) Use 4 subintervals to ﬁnd upper and lower bounds for the area of
the region under the curve y = 16 — 4x2, —1 g :r S 1. 1
(b) (8 points) Approximate / 1 16 — 4:1:2d1v by a Riemann sum with n terms. (You do not need to evaluate the limit of the Riemann sum.) Bonus on next page. I X
J ‘C (X) : (wax? f’hg) : (lkzx)a—XQCI%ZX)IZ
ﬁr.—
(wax) sow UW‘W z CHM)‘ C H‘“ )4
r. l’JY _________"—‘ (Hay? (Unﬁt C—Q 0 +920 4‘0 (1—90] “I’M—’—
Qkax )" t: ‘34. (IFav )5 N gl,()()2,0 :7 Wm atwe Mm»! a'l/L 1L1 {)0st” C‘) .C/QI {'3 Q/VL Poahj‘
3 M 41%): ' S’Wut
X’Q‘” x—aoa WC
SWWL ~15 WK :5\ )
vi 4 4 J Y70
7‘ S % 5 ¥ J/VVW WV
,__,. :0
Sat/2x3 *LJ Saw W Yaw X
/QJVVV~ Cum: Uxﬁwqﬁ) __ Hz/VE:
oo aO ._____ : 1,
Y") V9 )<~I (’12) x9” ('l/ T P R fL
_.=__=._ v IJ
H % H JR ‘7 4v» a
J; V=ﬁll
J 2
V¢§nrzh=§v=éﬁk3 _ 1T“ 3
'4‘ Wk 3X
2 \ ‘L
v, g—Z—{E )_. 3
away 1 3
“‘ “3.x ,Y70
Qty: [g0 ‘9)(1
M 3 Av [00 L 7.. 3—D SDSl/
Ext/0:9»:DX 57X:§=9X:E_ 0/3 3
To wad/.3 M Cavvﬂsfmoqo +0 {(4 Auk/tn W)
CW‘SMU" (>51va (AMI/J” a; O W?“
+ ._
V(§0\WMW«;WJ—gm WKWJSMMIJ
UM, SWCU. WW0}. 5%) M o‘bsiw M a} M {Dom}.  ‘3’ :50
“33%, M 3: EL? “7.5 Li
3(5N93)3
— LOJS _’9_
” 3’2" 5 ...
View
Full
Document
This note was uploaded on 11/30/2010 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas.
 Spring '06
 McAdam

Click to edit the document details