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# DIFFERENTIAL CALCULUS M 408K

UT

GPA 3.67

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This 13 page Class Notes was uploaded by Reyes Glover on Sunday September 6, 2015. The Class Notes belongs to M 408K at University of Texas at Austin taught by Staff in Fall. Since its upload, it has received 43 views. For similar materials see /class/181498/m-408k-university-of-texas-at-austin in Mathematics (M) at University of Texas at Austin.

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Date Created: 09/06/15

M408K Exam 1 Review Sections to Study Pre Calculus and Algebra concepts are fair game Chapter 1 1 5 16 Chapter 2 2 1 2 2 2 3 2 5 2 6 2 7 28 Chapter 3 3 1 3 2 3 3 34 Multiple Choice 1 If 6 sinz 7 cos I then nd f 0i Al 72 Bi 71 Ci 0 Di 1 E 2 2x240 3i Deterrmne l1m A5 mi Al 74 Bi 71 Ci 0 Di 1 E 2 4 Which of the following satis es 0 lt f z lt lt for all z 2 Al 6 Bi 612 Cl 6 Di 627 El e 5 Which of the following functions are continuous but not differentiable at z 0 ll 113 Hi 91 llli hz Al I only B H only C l and H Di H and III E ly H and Ill QxiS 7i Deterrmne lungcn00 mi AA 72 BA 71 CA 0 Di 2 El DNE 8 If 621quot nd f3i Al 6 Bi 9 Ci 66 Di 69 El 8 21 9 For What point on the graph of y 16 is the tangent line horizontal Al 717e2 371 75 Q 1220 Di 5 El 162 27 2 M408K Exam 1 Review 2 10 Determine y if y 333 AA 9 752 BA 9 7532 CA 9 Tilly DA 9 flp E y iL12 11 Let f be a function de ned for all real numbers Which of the following statements about f must be true A If limxgt2 f z 7 then f2 7 B If lim 5 73 then 73 is in the range of C If lirngc ne lirngcmner then existsi D If hme fx 1me 101 then limees fz does not exist E If lirngc 4 does not exist then does not exist The graph 0 39fhc cH nepids HM datum oi i The gvoeh a we Nnchnn 15 Ebown m m 39Rgm mm cCi tment 04mm 1 it True M408K Exam 1 Review Part II Completion Determine the following limitsi 17 x 1 1 1i limxal 715 2 l1m mgt0 7 W 3 lirngcaa 503 4 lirngc o I sing s 2 23 2h 373 5i l1m A74 50514775 6i llmh o 1000 7 11mingt00 15 t 8 If a function f is discontinuous at z 4 which of the following must be true ll limin4 does not exist Hi does not exist llli limx t y limin4 lVi lirngc 4 y 9i liming 260575 2 is equal to the derivative of what function at z 0 2 10 If I l 47 I gt 1 then determine limgcnl 6 7 z I g l 11 If lirngc g 7 and lirngc g 91 5 then determine 292 liming 0075 i 12 For what values of k will lirngc g EQEETSJrk exist 13 Find all horizontal and vertical asymptotes for iii Determine the following derivatives 14 15 e cosz 16 y 503412 17 y 18 fz a 19 y 1292 M408K Exam 1 Review Part II 2 20 ysin 21 yz211 22 y 213395z 3395tan3i513i52 23 y 1cosz 24 Find the derivative of y ff in terms of f g h f g and h Where f g and h are functions of Ii 25 If sin3 I determine f zi 26 Find the slope of the tangent line to the curve y cos 21 at the point Where I I 6 27 Which of the following functions are NOT differentiable at z 0 Iiy4712 If yz Hiyz IVi yz 2 Vi y sin21 271 zgl 28 G39 th fu t39 1ven e nc1onfz I27117 zgt1 determine Whether the function is continuous differentiable neither or both at z 1i M408K Exam 1 Review Answer Sheet Multiple Choice 1 E 2i SKIPPED 3 A 4 B 5 C Completion 3i 7 sina 7 1000 8 IV only 9 2cosz C 10 5 11 25 121mm 6 SKIPPED 11 D 7 A 12 B 8 A 13 B 9 D 10 A H CA3 i Vertical z 0 Horizontal y 0 2127101443 y 5 H F H 01 i COSI 7 sinz 16 81 amine 17 7m 18 7mg 5 19 20 imlchS 21 amp 12144 22 712i 7 3 51 4395 35 sec23i51 7 sinx 211cosx 0 g fghfgh7fgh h M408K Exam 1 Review 25 3 sinz2 cos2 I 7 sin2 I 28 Continuous but not differentiable 26 7 27 11 1V V 71 home Latin 7 Q1 quottr ft N ye ngfe q Mr an 0 90 1w 0 6 68 2 797 2 392 a 38 3 3 W Mt16 J C39f39 1 5 chasm 9 Km 4 b IE 1 904 WM ab a ICbn he an In889 p 2 30 A X zgt apz D 399 has m Mir emquot From 94 Au 6 00 I aqua omit 9 far was x 7 th be5e 65 MW com 0 0m Igt Hammad qu 2m j AV 6 19 cue Dram 3 w hodwuiag lu39t eWS Ltg wore Hum once i V 53 K612 S l 5 6dxz K6 060 A m EX D amp IAW LP be A row 1mm 9 mm Wm A OucL wager B m 5 Win 6 1mg Amiu8 and WW A 15233 6ltgt 6 Q 4 M dwiw 364 bu 6 5 4quot A gawk 6 f M 6amp3 we e A ga gamma WW 5QC7agtx was an 4 xiiw 4 B A 3 we 5 o 7c 3 g 7amp7 W 3 Dm lk R 13 Rugz 1 R D x3113 I 3 DOWN 03 1 R IV 330 J3 Ramatdamp 4 R gt Ne w A 7mm WW 0 cgt xiii 29 game 4 I er39r e 391 M a 4W 5 31 x quotm Dam 3 4 5 W 4 PW w 49 3 3 mid 5 am aquot quot gt g I Pub Ultra 5amp2 1amp3 4 x5 if39 3R 25 M was 773 53w A A R w W agar 3 2 a Add A ASE mu 3qu An u 0 19 S6 A 30V A

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