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Unformatted text preview: MA 1021 A ’07 Instructions This test is closed book. Calculators are not allowed. Part I  Basic Skills Final Exa II 5 A01 Heinricher, A (PLC)
A04 Wasyk, R (8:00)
A07 Hrynkiv, V (1 :00)
A10 Tang, D (10:00) A13 Tang, D (12:00) Please Circle your Section A02 Abraham,J (3:00) A05 Blais, M (9:00) A08 Malone, J. J. (1:00) A1 I Masamune, J (2:00) A03 Hill, M (8:00) A06 Burgos, C (9:00) A09 Tashjian, G (1000) A12 Hrynkiv, V (3:00) 1. 2. 3. aFmd——ny= 5. 6. 7. Part I — Basic Skills Work the following problems and write your answers in the space provided. Use the
scratch paper provided for your work. You need not simplify your answers. No
partial credit will be given for these problems. t 3 5' ﬂ.“ 32.x '3‘ —~ Findgif y=7+2\/;+3x4—§. Ans. W + #1“
x _ —“_—*— Find i): if y=x5tanx.
dx Find 3% if y=esi"x. Ans, e; {3053K dy x3 ca 2—5x' 1%»7
Findgif'y=h1(x2~—7x+18). Ans. Xlﬂxﬂg “Hle Ans. 711' ~5 £31“ . . 2 3
Fund — If x + =0.
a J’y Find an equation for the tangent line to the curve y z x2 + 5x — 4 at the point (3, 20).
Ans. y "2 X “" E3 Part 11 Work all of the following problems. Show your work in the space provided. You
need not simplify your answers, but remember that on this part of the exam your
work and your explanations are graded, not just the ﬁnal answers 8. Evaluate each limit or show it does not exist. (6 points for each part) Vx+2—3 a. lim
x—>7 g; ism ><+am3 ) {M2 +3 r [EM 5:?” a
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M o x wee—mam... "2:: .——. i O 9. For f (x) = 2x2 + 7 , ﬁnd f'(x) by using the limit deﬁnition ofthe
derivative. (12 points) 10. A boat is sailing directly north from an island at 20 mph. A second boat is
sailing directly east from the same island at 25 mph. At this moment, the
ﬁrst boat is 40 miles north of the island, and two boats are 50 miles apart
from each other . How fast is the distance between the two boats changing
at this moment? (15 points) ll. lﬂé‘éﬂfwi In this problem, you will analyze the curve given by f (x) = 3x4 — 4x3 (This problem is worth 20 points) 21. Find all intervals where f (x) is increasing
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ties + {mgreagivlj 6m 0,5’06) b. Find all intervals where f (x) is decreasing @ecrwwj on (“09,ej
W (a) a) c. Find all intervals Where f (x) is concave up way «a. 15¢ka Mg 251‘ Concave U? {33"
(“092% W (16,09 (1. Find all intervals where f (x) is concave down meN/e 65W” OW (0)273) 6. Find all local maxima and minima of f (x)
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fin (zér/LOQ) bahgait (“j (a;me Mi? 3 f. Find any inﬂection points of f (x) Iﬂg'leaﬁaw Pathl Q x7210 .SthCQ.
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IIIIlllumllllllllo II... . IIII... 12. Find the maximum possible volume of a cylindrical can if its total surface
area (including the top and the bottom) must be equal to 540%. Note that
the area of a circle is m2, and the area of the side of a cylindrical can is
27rrh, where r is the base radius and h is the height of the can. (16 points) Zﬁr‘z«h ZWFL’X': Vt; Erik. r: NE a“ egg—FF“ <5: Weﬂa‘ﬁue «bl/"a?"
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‘3 0‘3“. Find the derivative of the foiiowing ﬁlnctions. (6 points for each part)
a. f(x) = sin5 (x2)
: ‘+ _ a; gSln COS (Xi) —.—. 10% M (x1) w (2*) b. f (x) = 3cm”
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;< ’— ', ){CDSX ((—usﬁnx>(/qu§)+
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g; 128‘ nD/(a)=— i429 )
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This note was uploaded on 10/13/2009 for the course MA 1021 taught by Professor Tashjian during the Spring '08 term at WPI.
 Spring '08
 TASHJIAN
 Calculus

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