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by: Reyes Glover


Marketplace > University of Texas at Austin > Mathematics (M) > M 408C > DIFFEREN AND INTEGRAL CALCULUS
Reyes Glover
GPA 3.67

Katherine Davis

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Katherine Davis
Class Notes
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This 5 page Class Notes was uploaded by Reyes Glover on Sunday September 6, 2015. The Class Notes belongs to M 408C at University of Texas at Austin taught by Katherine Davis in Fall. Since its upload, it has received 521 views. For similar materials see /class/181423/m-408c-university-of-texas-at-austin in Mathematics (M) at University of Texas at Austin.




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Date Created: 09/06/15
M408 C Pra I nstiuctor Guoliang Wu ctice Final Examination Name UTEID Problems 178 10 11 12 13 14 15 16 17 18 19 20 Total Grades Out of 40 5 5 5 5 5 5 5 5 5 5 5 100 1 You need to reduce your answers to the simplest form for fall credits 2 Textbook notes or calculators are not allowed 3 You can nd the formula sheet on the next page 4 The real exam will have the same format 8 number of questions But the di icalty and percentage from each Chapter may be di erent Good luck Limit Formulas 111 I 1m x7gt0 lim 17 cosz 0 x7gt0 z 1 17 cosz 1 117 12 7 E hm ln1 z 1 x7gt0 E 11 lim a lnaa gt 0 x7gt0 11 1 lim 6 7 71 x7gt0 Differentiation Formulas I7 nzn sin z cos I cosz 7 sinz tanz sec 1 2 cotz 7csc z 2 secz secztanz cscz 7 cscz cotz ET 61 a a lnaa gt 0 lnz arcsinz 117 71lt I lt1 arccosz 7 i 71lt I lt1 arctanz 1 E 1x2 1 112 arccot z 7 Basic Integrals fzndz zn1 CJL 71 f de ln z C fcsc2zdz 7cotzC fsecztanzdz secz C fcsczcotzdz 7cscz C V arcsin C I af z iarcta n 3 C fseczdz ln sechrtanz C ftanzdz ln secz C fcsczdz ln cscz7cotz C fcotzdz ln sinz C Algebraic Formulas 13 WWW 7Iyy2 137 y3 1 7yz2zyy2 acy3 13 312y31y2 y3 I i y3 13 i 312y 3zy2 7 y3 Trigonometric Formulas csc97 sec9 6959 we 7 22 cot9 605g sin2 9 cos2 1 1tan2 9 sec2 9 1 cot2 9 csc2 9 sin79 7 sin9 cos79 cos9 tan79 7 tan9 sin7r2 7 9 cos9 cos7r2 7 9 sin9 tan7r2 7 9 cot 9 sin7r 7 9 sin9 7 sin7r 9 7sin27r 7 9 cos7r 7 9 7cos9 cos7r 9 7 cos27r 7 9 sin37r 7 9 7 cos9 sin7r 9 cos n 7 9 7 sin9 7cos7r 9 Addition and Subtraction Formulas sinz y sinz cosy cosz siny sinz 7 y sinz cosy 7 cosz siny cosz y cosz cosy 7 sinz siny WWI 7 y sinz cos y lsinz 7 y sinz sinz siny cosz 7 y 7 cosz cosz cos y cosz 7 y cosz Double and HalfAngle Formulas sinZI 2sinzcosz 2 212cos2z71172sin21 cos 21 cos I 7 sin 7 212mm tan21 7 litangx Sin2z 1 0st 2 COSz I itcgsh Functions of Angles Find all the critical values of a3 m5 CalC3a18exam 139 x 2 001 100 points 4 Find the value of f391 when 2 a v5t1 3 5 3 a 3 i 1 1 4 m m 3 5 4 a 3 7 2 1 4 f a 5 1 3quot1 Elm 37 f Na 2 we l 4I 697 2 5 3 5 391 7 7 1 7 m V6 4 6 Wm w6 s z 3 CalC8a21exam 002 100 points CaIC4b1 exiim 004 100p01nts Evaluate the integral Determine if the function 1r2 I 0 2mcosxdx x x31 L I l satis es the hypotheses of the Mean Value Theorem MVT on the interval 1 2 2 I 2 If it does nd all possible values of c in 1 2 satisfying the conclusion of the MVT 3 I 77 2 1 c 4 I 1r 1 2 c 1 5 I 77 1 2 3 c 0 6 I 27r 4 c 1 CalC4a01exam 003 100 points 5 hypotheses not satis ed Ca1C4d46exam 005 100 points Use concavity to decide which of the follow ing is the graph of 31 f0 Tm 1 2 3 H j j 4 1 CalC5b01exam2 006 100 points When f has graph R1 express the sum I rm 2fltxdx in terms of the areas A1 areaR1 A2 area R2 of the respective lighter shaded regions R1 and R2 1 I 3A2 2 I 3A1 A2 3 I 3A1 A2 4 I A1 5 I 3A1A2 6 I 3A1 A2 CalC6a17exam 007 100 points The shaded region in y is enclosed by the graphs of y 112 y1 3211 Find the area of this shaded region 1 area 11 sq units 2 area sq units 4 3 area 3 sq units 31 4 area E sq units 32 5 area 3 sq units CalCSe36exam 008 100 points Evaluate the integral 7r6 I cos2msinmdm 0 a i 00 1 w I i 1 4 i on PH COMO mm O39HH H


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