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: Math 1A Second Midterm Exam November 6, 2000 C. Pugh Closed books, closed notes, no calculators.
Please stay in the exam room until 10.00 am. Except in Problem 1 SHOW ALL WORK. Name
Section 1. (25 points) Answer True or False. +5 for correct answer, —5 for incorrect
answer, 0 for no answer. : VE<.8. { /; 62‘” — 1
‘ The hyperbolic tangent satisﬁes the equation tanhzc = 2/
e I + 1
. d . , t V *
There ex1sts an a: E (0, 1) such that d—((a:(:c — 1) s1n(eI)) = 0
:1: J w a x
As :1: —> oo, / —> oo.
ln(:1;“")
T 1 + le3/2 is an antiderivative of (3/2) ﬁll/2. 2. (25 points) A 52 pound red herring hangs from the end of a rope. The
rope is 60 feet long and passes through a pulley which is 33 feet off the floor.
A man holds the other end of the rope in his hand at a height of 3 feet off the
floor. He runs away from the hanging herring at 5 feet per second. When the
herring is 10 feet below the pulley how fast (in feet per second) is it rising? . ’T" . . 0 w W
Explain. , » \ ~.~ x g/ux “" 53> a
, A3,, L w" ; k, I ,3 _.. It I;
i x ' a 2, ﬁiii? cl“, " ‘ L ..w i I i' , v‘ ‘3 "
ﬂ 1: ‘ ; v i
\ .. , ” ‘" . ,3 . ‘ L
R
1 \/’/M
l ~ , I C
ya»: :_ (vi) a
”i ix; ! “I x
V\:"\ \. i {N I: ‘ ”" f :3
«.347. a} Q i E.
, 4 f) t :
“if"?
I
i r M: {\D 40/2; /‘/ 3. (25 points) Consider the function f (1‘) = 835 — 62 :1: 
L_ w k , Maw.“ 3? ”we, . my?)
(a) Find its intervals of increase and decrease, if any. i
(b) Find its local and global extremes, if any. ( ’ \
.., . K W, ,
(c) Find its asymptotes (vertical, horizontal, and slant) if any. Im’ .
(d) Find its intervals of concavity and points of inﬂection, if any.
(e) Using the data from (a)  (d), graph the function. 6)
' . ~_ “‘’ 1 v t
, \ 2 w { i ._ , O
K .i ohm '
, “ . ‘ @
C  e il l f ‘ H
l 1‘“, W H \ ~— l 6
x ; ihu _ an ( “0°, 0) @
I 1 0 if
i \ \ ' ‘ >4, Q
r; r i , 4. (25 points) What is the largest volume of a right Ciregular cone inscribed in a sphere of radius R? Explain. ‘“ ' ' ’ ' ”W lABxféglx'l ‘1 IQCT
'» L V1 ) : \j l K \ i: ”a i wk» ( ‘ V , {'3
i;
w ,1 a
l H I ' ”
>1 r
‘ 1 w , x;  , r *‘l' x
/ l \\/ \ \\ u,
l l , \Z w
J ‘ / a 5: 4" {Jig/4
' t /
\‘ .\ "a“ l l \ k
‘ ‘3
of“... " — J ‘ “M. a...“
Jr 2 v » a .
v? 1 ~:‘\ \ﬂ " .4 !
i7 f . y r“.
availkl»: _, L. '3 g3 h,“ r if K ANSWER. ‘ *~ A i): r « ...
View
Full Document
 Spring '08
 WILKENING
 Math, Calculus

Click to edit the document details