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MA 1021  2006 A Term Section 10
September‘ 21, 2006 Quiz  Sections 3. u , 3.7, 3.8 Please note that the ﬁrst problem has NOT been done for you this week! I. Allstudents taking MA 1021 in A Term 2006 will take a common ﬁnal exam on Wednesday evening, October 11, 2006, and should
have already cleared their calendar for this time. 01' FALSE {please circle the correct answer  2 points) (05 ~— 4; Give two angles (in radian measure) where the sine of the angle is
equal to V2. (2 points) You live next to along, straight river. The river is 8 miles across
(wow, that is a BIG river!) On the Opposite bank, but 10 miles
downstream, is your school. You wake up one day, and are worried
you may be late to school. You can swim at a rate of 3 miles per
hour, and you can run at a rate of 5 miles per hour. What is the best
strategy for you to get to school as soon as possible? (Oh, and one
more amazing thing about this river — it has Q current!) (10poinrs) .i.
3 (ShXL 5 1m ’9 x
y 1321. .
"‘ ,4/ c 19 ANSWER: SWIM
O 3 15" 11; 4:. Poinl 4 "ﬁnc;
o the...
10 q, 61” Cl szr ’l‘b hum)
6 /3 + /5 7 r; 6" SMCIl‘ﬂr run 'Hu “Mannan
‘ £5 6 Muir;
{0 Just ,_ Cle
__..a"" "" ..___.— 3 [5" 7. Show that Dx [sec x] = secxtan x. You may use the fact that DI [sin x] = cos x and Dx [cos x] = msinx, if you wish. (8 points) (of)! ewx A cylindrical can is to be constructed with an aluminum side and a
copper top and bottom. The can will have a volume of 64 cubic
inches. Copper costs 4/1: cents per square inch, while aluminum
costs only 1 cent per square inch. Find the dimensions (height and radius) of the cheapest can which meets these requirements. (10
points) V: ﬁrfL; '3) 142.. £1 77/1" Cask 9 @‘TKQ—XI‘ZT ) # (Zfl‘rk) (I) “dyerAl's; has; Inn“! 4.. caged
m2. cowg‘pmal; 7’1 4 ~~ I 605* cud(e.
“global W’NMUH ’2 in. SmA/hjl l9 ovax. a.” Pajlhve real n"v‘~9¢’:. 23W!!! Cln— Lona/4‘ r7: 2 “and LI '3 A b—I/ﬂ—x 9. Find the derivative of each of the following functions (5 points each) a. f(x) =(x3tanx)—[Sinx] COSX 2 ___,. n 10. Find the derivative of each of the following functions (5 points M) 2
b. y = x(x ) (hint: use logarithmic differentiation) 9“ WM We) *****a:********* END OF QUIZ **************** ...
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 Spring '08
 TASHJIAN
 Calculus

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