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Unformatted text preview: Exam I
Math 408C: Differential and Integral Calculus
Unique Numbers 55420, 55425, 55430 February 22, 2011 ke Instructions. Circle your unique number above. Read and follow all directions. Ask for
clariﬁcation if any problem seems unclear. You have the entire class period (75 minutes)
to ﬁnish. You must show all your work. The exam is worth 40 points. Please note: 0 Unsupported answers will receive zero credit. 0 No notes, books, calculators, or mobile phones are allowed. 0 Be honest! Cheating on any problem voids the entire exam. Name and UT—EID 1. (5 points) If a is a positive constant, compute gig at a point (x,y) on the curve 5 4 “
x2 + (a) = ‘5 .me’l'r"? ﬂ'mrem‘b"”*°l
a a Qx+5%)q'zl]% I: o (a .‘s Start Somt> C/ov‘3W‘ev'
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Math 4080: Differential and Integral Calculus
Unique Numbers 55420, 55425, 55430 February 22, 2011 Name and UT—EID_ _ .kf LEM Instructions. Circle your unique number above. Read and follow all directions. Ask for
clariﬁcation if any problem seems unclear. You have the entire class period (75 minutes)
to ﬁnish. You must show all your work. The exam is worth 40 points. Please note: 0 Unsupported answers will receive zero credit. 0 No notes, books, calculators, or mobile phones are allowed. 0 Be honest! Cheating on any problem voids the entire exam. 1. (5 points) If a is a positive constant, compute ﬁg at a point (x, 3/) on the curve 5 4
x2 + (g) = _3 .mell’lIV £‘%W*VVMI
a a 72kg 3!; at low/‘ Cw; I O (a .‘g Susi Somc> C/O" [rm $:nQ§X)/cp$éfX)
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 q I  2. ( 5 points) If it exists, compute lim
$40 (5383) Show you?~ work and explain your reasoning! .....——_...,.~.._Mg M... v ‘ .,.A [3“ : I I
)(>o X I 4,.. _ m. ...._.,,_ .._.,_.—~—. “Munr‘w
/ ____ know {414* LN! 4,4 {yawn
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r7 L We W3” 3. (5 points) Compute the best linear approximation to the function 1
9(m)=¢%ﬁ : (x‘+ 7) Z near the point (3, %) Pom/w “Slope ‘tcﬁwmula;
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If . 4. ( 5 points) Use the deﬁnition of the derivative to compute f’ if _:1:—1
_:c+l' f (x) You will receive no credit if you use dzﬁerentz'atz’on rules! I 1,“ $044.) —~f(x)
DzﬁmiHon J f (X) = ’ ’lbo h x+hI., x" I (w. 7:717 x+I Cu (A Comm"
' ___________’—I—'
‘i: M90 H MawMAW! I». I X+H~I x+')_ X“)(X“+’)
: 4.). 7 m7, T+I 2w HAN [ Xz‘lkX‘X4’x—Ik’l — (xiuﬂudqvl)
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v w ‘ xyMI (XH "9
(A¢0)/7 ( ) > ‘: .E—f'
om)‘ (am rel: cut . . . 5. ( 5 points) Compute 2 041 m W7 W H, J“ +4”): @ i(gosé> WW4 90 695+ . .L) 4( (5m +) 3 “1‘! 2; Sad Srn‘d')
(L16.'H
rule I
i \ ‘ race“ {1‘
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S;n‘£ ; \ + Csczlt) . (4:83)) SCH16") (‘ Sinfﬁ‘jng : uét(f\_ (Stq(+) ’ ‘
. ‘ Sm ff) Le+ A Loft 50‘4"“ We. 6. ( 5 points) A spherical balloon is inﬂated from a tank that releases helium at 30m3/sec. At what rate is the balloon’s surface area A
changing when its radius is r = 12 cm? 7. (10 points) Sketch a graph of the function 1 9°”) = m, and ﬁnd all (any) points where it: a has a vertical asymptote,
None [I 0 or fails to be continuous,
New Auto/"HS! 0 or fails to be differentiable. gm 3(3):! «4
I»: an): ‘60) =) I J x93
3 "3 mﬁMuh! ‘1'“ "=1
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This note was uploaded on 08/18/2011 for the course BIO 1406 taught by Professor Bostic during the Spring '09 term at Austin Community College.
 Spring '09
 BOSTIC

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