exam1key - Exam I Math 408C: Differential and Integral...

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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' {l/ q 53.5- 303: —2x 0! oLX ll, J’h ~14” atx” 5‘6” Exam I 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) X90 {4‘6 Cirdrl 5h” (at-leis! [-M Sin 8*) W590 , VJ 7- X90 smflu) IL 1m 9‘4"). i:— ' COSQPU' 2 :X.” mom ‘I 3 [m 53115). (m 1:: . (m wqu I; x“ 3x x“ Swen) X~>° — "5 [mm “(M I I v " ° . H 9&6" . 973190 sx 7702mm ‘\‘\H m /" 3m: ‘— 2 c I o i ‘" \m VVVVVVV M - 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 Yo“ Ara” + [Md 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; - $3375) (x43 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) Dzfimi-Hon J f (X) = ’ ’l-bo h x+h-I., x" I (w. 7:717 x+I Cu (A Comm" ' ___________’-—I—' ‘i: M90 H Maw-MAW! I». I X+H~I x+')_ X“)(X“+’) : 4.). 7 m7,- T+I 2w HAN [ Xz‘lkX‘X4’x—I-k’l — (xiufludqvl) [ILA a WW 51 lo; - (X+I.+I)(X+I) ~13“ Qty”, 3 km [II—+7255»: (“:00”) 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‘ GM Hzoésmfl _, costilshe)‘, tort ' 2*; (Dig) C 56235)) PM (a! .—- (Sinifi 5 ‘ Srw'fl) ——3ws‘66) S.»‘h’(£) —; (of(+)'Zc€c'l+)'6(““‘”'”‘°) S;n‘£ ; \ + Csczlt) . (4:83)) SCH-16") (‘ 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 mfiMu-h! ‘1'“ "=1 l .094- Hewflvu % £0“ ...
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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.

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exam1key - Exam I Math 408C: Differential and Integral...

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