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# Calculus MAT 021A

UCD

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This 9 page Class Notes was uploaded by Otilia Murray I on Tuesday September 8, 2015. The Class Notes belongs to MAT 021A at University of California - Davis taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/187442/mat-021a-university-of-california-davis in Mathematics (M) at University of California - Davis.

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Date Created: 09/08/15

MAT21A Sections A01 A05 homework set 1 DATE september 28 2012 This rst week s HW problems are 1 2 3 4 5 6 7 8 15 16 23 on page 11 and 12 in the textbook Niels Gronbech Jensen UNIVERSITYOF CALIFORNIA DAVIS CALIFORNIA95616 TEL 5307525335 MAT21A Sections A01 A05 homework set 2 DATE Odom 5 2012 The second week s HW problems are Sec 21 561011 Sec 22 1 3 5 6 12 18 20 21 22 31 32 33 35 42 51 63 64 80 81 Sec 23 12 16 17 21 25 33 34 38 47 48 57 59 Sec 24 212325 29 3132 3539 Remember to ask questions and use of ce hours as much as you need to Have a great week end Nie1s Gronbech Jensen UNIVERSITYOF CALIFORNIA DAVIS CALIFORNIA95616 TEL 5307525335 Solution to MAT 21A Practice Final EXAM Dr Qinglan Xia Name Grade Instructions This is a closed booknotesfriends exam No calculator is allowed Problem I Multiple Choices 60 points total 3points each Please ll in your answers in the following table Problem 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Answer mB B D A c D c c A A 3 13 0 A A B D D c 1 Find the limit of does not exist COW Gum NIH t O 2 Find the limit of 1A 5sin 2x 7 2sin3z 1131 2 sin 7x 7 5x 5 0 W gt O mlmwmmlm 3 Find all asymptotes of the graph of i 2z214z20 ix z 6 A vertical z 72 horizontal y 72 B vertical z 3 horizontal y 72 C vertical z 72 horizontal y 3 D vertical z 3 horizontal y 2 4 Locate and classify all the discontinuities of the function f de ned by m f96 5 95 0 A f is continuous everywhere B f has jump discontinuity at z 0 O f has oscillating discontinuity at z 0 D f has removable discontinuity at x 0 5 Find the derivative of f when i sin z 7 cos x f 96 sins cos A f 96 13 f 95 W O f cosmsinm cosmisinm D f z 2 sin mcos m 2 1 2 sin m sin mcos m2 6 Find the derivative of f when f lncos 2x A f sec 2x E f 2tan 2x C f i 72tan 2x D f tan 2x 7 Find the derivative of f when f 3x sin 2x 7 2 cos 2x A f 5s1n 2x B f 3xcos 2x7sin2x C f 3xcos 2x5sin2x D f 6x cos 2x 7sin 2x 8 Suppose x 7sin8 g 9 Suppose y x2 1m7 then is A x2 1 1 2 1w lnz2 1 2 1wln2 1 M2 27171 lnz2 1 22121 bop 10 A Child ies a kite at a height of 50ft7 the wind carrying the kite horizontally away from the Child at a rate of 26 How fast must the Child let out the string when the kite is 130 ft away from the Child A 24 B 26 sec 0 25A 550 D 23 11 Suppose fx 36m 7 7ln1 7 2x 3 Then7 the linearization of f at z 0 is A Lx 17 6 B Lx 717 6 C Lx17 7 6 D L 6 12 Suppose fx x672 713 Then7 the critical points of f are 7 13 A 7077 13 03 C z0 D x3 13 Suppose fi x2x17 x20 7 gz2717 xlt0 Then x has local maximum at x 0 C D 01 is an in ection point of f 14 Suppose f 75z21n 34 x has no local extreme points has local minimum at z 6 12 712 m has local maximum at z e has local minimum at z 1 15 Find the function f Whose derivative is 2 sin 4x and Whose graph passes through the point 07 2 72cosx2x24 13 f 2sin42 C f 2cosx 2x2 D f 2sinz1L 2z2 2 16 Suppose f 2 715ew Identify the intervals on which f is increasing A f is increasing on 70075 and 3 4 B C D f is increasing on ixE f is increasing on 700700 f x is increasing on 753 17 A 12 gtlt 12 square piece of cardboard is made into an open box by cutting out a square at each corner and then folding up the four sides Then7 the maximum volume of the box is A 128 B C D 2 144 72 18 A manufacturer of digital watches determines that the cost and revenue functions involved in producing and selling z watches are 2 C96 1200 1395 and Rm 7595 7 9 respectively How many watches should the manufacturer produce to achieve maximum pro t A B C D 74 52 64 62 19 The limit A B C D 11x2 lim 7 ma0 cos x 7 1 does not exist equals to 0 equals to 22 equals to 722 20 The limit COW llnm 3133596 1 does not exist equals to 0 equals to 6 equals to 1 Part ll 50 points total7 10 points for each problem Please provide details for the following problems 1 For the function f de ned by ln12m7 lt 0 f 72 z 0 272 H1 m gt 0 a Find limmnoi 1 17 2 9 2 lim fm lim U lim i2 mHO maO maoi 1 b Find limmn0 1 f1 2727 2 c Does f have a limit as x approaches 0 If 77yes 7 what is the limit Solution Since limmnoi f limmq0 fx 72 we have the limit ling f 72 d ls x continuous at z 0 If not7 what is the type of the discontinuity Solution Since limwno x f 07 we have f is continuous at z 0 E0 Problem 106 in section 44 See page 253 in the textbook 9 Find the equations of the tangent line and the normal line to the graph of the ellipse 4x2 y2 4 at the point P712 Solution Take derivative with respect to x on both sides7 we have 8 dy 7 29 i 0 dj 78x 74x dx 2y y So7 at 13712Ag7 we have dy 4 ii 2 a T E Thus7 the slope of the tangent line at P is l and the slope of the normal line is 7 The equation of the tangent line is 2 1 2 4 ixgi 27 ie 7z7 9 V3 2 9 3 The equation of the normal line is 4 9 Suppose fx x V16 7 x2 Find the absolute maximum value and absolute minimum value of f on 04 Solution 72x WWW m Set f 07 we have x 1 x167s2 17 m 7 0 z m 2 1672 2x2 16 x x in 074 Thus7 the function f has only one critical point m xS in 04 Since f0 4f4 4 and f Mg mdm the absolute maximum value is maX 444 4 While the absolute minimum value is min 444 4 Identify the intervals on which the function 1 f git 72 5 m 71lx 71 is concave up and concave down Find also points of in ection of f Solution When z gt 171 7 1 z 7 17 so 1 f g4725z71x71 4725z272z1 x472x476 Now7 4 x z372 fquotz 42gt0 So7 f is concave up on 17 Whenzlt171x71l7x71so 1 fx 47257x71z71 1 1 x47z2572271gz472x22x4

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