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# Review Sheet for MATH 1431 with Professor Morgan at UH

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This 57 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 30 views.

## Reviews for Review Sheet for MATH 1431 with Professor Morgan at UH

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Date Created: 02/06/15

Midtenn Review Evaluating limits of basic functions rational functions and piecewise de ned functions Evaluating the variations on sinuu type limits Continuity Computing a derivative by using the de nition of derivative Basie derivatives using the sum product and quotient rules Derivative of trigonometric functions I Chain rule I Tangent and normal lines I Implicit differentiation I Related rates I Neu1on s method I Differential approximation The Midterm covers nmtenn duougJi section 39 n mu No39r have material from section 2 2 the pth ofscclion 20 covering the pinclung theorem or me falling object problems from section 3 gt1 Jan 1711 10 AM Good sources of practice problems 0 Examples from class 0 Popper questions from class 0 The basic homework problems The basic online quiz problems The list of problems in the following slides Jan 1711 10 AM Limits Jan 1711 05 AM lim2x2 3x1 2 32 3 3 H 12 3 xgt3 0 lim sin2x 31m quotA T s th H Sic 1 xgt72 3x 3C ZB D U Zx l 2 3 1 5 11m H3 x2 2x1 32 23Y Ll Jan 1710 30 AM lim x24 l x 2x23x 10 quotquot 391 x 1D n x b39l x 1 AS IIAAQJ QI MH AVA gHL L 31 339 33 7 W x91 MIX 4 Me H2 x2 3x 10 Ill 0 Jan 1710 10 AM 2 U limx 1 M X 7 40 amp H1 x2 2x1 x9 392 WW l I t X MALhim MAY 0 43mm 4 2 0 gtlt 11m x 1 I M 9L 339 f l39 I IMAL VQI Mquot an r 7 a l O 0M 7 Jan 1710 10 AM lim 5x H0 sin3x 39 livvimam iorm 3m 1 O S x M sinu m37 0 hm L A S at 111643 395 Jan 171011AM I I lim 51n2u 3M 5mm I i 11 we sing u bo s mbw we nLquotl39quot Wquotd 39 u 4M 4 sum u M 397 quot v M WW smGA u bo u shrub l 2 3quot J39 M 3 ubo Shrub K z 392 3 Jan 171011AM lim1 005u km pmmeuwqu w Elli Ho 2M2 0 2 10 50 IAgt o u u 2 wmrm mad I 1 hm a 4m M 1091 Um s mu uao 1u1qsu 39 l 1 lg uw l 57 v I H Jan 171011AM lingxcot3x ml 1 5151332 M Ma H 150 Sid u m 1 usth hm 34 m U90 S1nk 70 s39m 2x 9 quotdukum39mm a 4M hm HO KM L 3 Jan 171011AM 10 Continuity Jan 1711 05 AM 11 2 Give the set on which the functionfx x 7 is continuous Rational functions are cuntinuous everywhere they are de ned Z xvm0 p mm 4Mth 1 A quot no r 0 XL Jan 1710 17 AM 12 Ax B x lt 1 Give values ofA and B so that the function gx 3 x 1 m mi Axl ZB xgt1 gm m 3m 4 H 3 ll am 36quot M 9 x2113 X I m Hf 2 rm fwd w 1 LH u is continuous 0 Jan 1710 17 AM 13 Ax 1 x lt 0 Give values ofA and B so that the function gx 1 x 0 w 28 JL mch x gt 0 is continuous gag am am 4 XquotD ll law 36 Xquot 9 x303 gt90 II TM R7518 rm A7913 w xvo39 u quot 43 l as 00 5m v 391 4 i PEG11quotquot Jan 1710 17 AM 14 Intermediate Value Theorem Jan 1711 05 AM 15 Use the intermediate value theorem to Show that the given equation has a solution on the indicated interval 2J 7 4x1 5X 7 4 l LZ W a A f is a polynomial so f is continuous 03 2 14 5 4 7 quot 432 1 It N 10 quot1 9 Since 0 IS b wee l M 0 quotll L efmdi39g i39l Me W1quot l mf39w39v mi VHMAL 31 a VALUEquot 1 7t bulemt W d 739 whare 43m 039 Jan 1710 18 AM 16 Use the intermediate value theorem to Show that the given equation has a solution on the indicated interval quot397 7 l 0 7 I l W 4 64 f is a polynomial so f is continuous x1 1 1 IMO l SW1 0 5 between Mquot 4m Merme at Vol44 Wrw bu ame WW 7 a VALUE dc bylmkut 71 M where 43M 0 39 Jan 1710 18 AM 17 Use the intermediate value theorem to Show that the given equation has a solution on the indicated interval sm 39 2 cosx x3 0 0 nZ J 4quot A f is a sumdifference of trig and polynomial expressions so f is Continuous 03 0 2o 2 hwy LoTTW 14775 lt0 S mce a 35 lethalzen 2M 1111 quotll L Mermdi 7 WW WW4 buarw m WIUL U 0 Vm all 7 bxhum e M 771 where 6 039 Jan 1710 18 AM 18 Use the intermediate value theorem to Show that the given equation has a solution on the indicated interval Zmnx I er4 r 643 f is a sumdifference of trig and polynomial expressions and tanx is de ned on the interval so f is continuous rm 040 o 3 Q mg 247V gt27 gt1 35 bahween o M 2 1w mermaid W WW Alva r W m a a V 534W lyL39i39quM o M q 43m S39mcvz l wine w Jan 1710 18 AM 19 Use the intermediate value theorem to Show that the given equation has a solution on the indicated interval 4 6 f is a sumdifference polynomial and rational expressions and the rational expression is de ned on the interval so f is continuous ms I n 1 39 m I n J 05 2 J7 7 L J Since 0 39IS b1 me lb M 739 1w me d W WW altarm k vHML U a vulva cg wan t m I when 43M Jan 1710 18 AM 20 Solve the inequality below 3921102J gt 0 V V J r A f is a product of polynomial expressions so f is comimmus 3600 Wl l vl 11759 Ho 4 JPM4 o gt 7 l 2 3 s L 03 3 gt0 40 H M Ma gt9 0 V2lun zngt0 ow Goo 13025 Jan 1710 20 AM 21 Solve the inequality below 239 l3i 5 3 0 W a F f is a product of polynomial expressions so f is continuous g 43 3530 wlnlm 110 X 7X 3 Oo o Iaquot 39 l x 1 o t J a g 7 3 ale 7 1 0 WIN3 SM INN l 6 44 4 0 gt0 4 O gt 0 2 13 5 3 0 M f E0J53U po l Jan 1710 20 AM 22 Solve the inequality below quot 2393 39 5 0 V I 6 f is a polynomial so f is continuous a 66 XSQrzH 33 1 2quot 3 x6 90 3530 alum lt0gt7lt m o 4o l t r l 4 7lt l 0 J7 I 2 Send 3m AWQWUG H7946 zo 0 gt8 Jan 1710 20 AM 23 Using Derivative Formulas Jan 1711 06 AM 24 Jan 1710 22 AM 25 sin2xcos 3x s mzxi ltquot COW and an s39m a pin y CA 3gt ZCAS2A T AVC 33mzgt35m3gtlt3 2 Ca537 ca zgt gt Jan 171022AM 26 i 2 UK 15 2 1 3 61 Zxcot 3x Jr 3 4 CD X f A dx 1 2y dxco dw SDMVA ZX csc3x2 If 1 ZCJDM3 Zj 1XCS3lt1397lt 2 c3 3v T JqLQsc 3 5 2 0044935 Jan1r1023AM Give the equation for the tangent line to the graph ofgx 2x2 3x1 at the point where x 1 eoiqlv 1 CH 3013 r C gt 393 7 mt Sis 239 3 0 m 3643 Lpt E 2 433 7 Tm WWWquot 33 7Xl Jan 1710 23 AM 28 sinx 3xcos2x2 1 2 d z B 3 0 2 H Cosva 36v3amp s 0254 OWL 1 39Wyl Cosx ZY DO 4 is 5101gtlt MB 3 cogGEgB ws m 2541M OJ 3 Jan 171023AM 29 2sin 3x tan2x5 5 1 s39m xh Mn ASf f sinw n2ltgt 4 5 1 s39n xH cm2xgt39 cos3gtlt 25 2M Jan 1710 24 AM 30 Find atx 2 where g2 3 f2 1 g 22 f3926 andf 34 iigm g cbgm ow at 7ltz wL w 3932gt3lt3713 393323 1 LWCZ 3 Jan 1710 24 AM 31 Find f g392 where g2 3 f21 g 2 2 f392 6 andf 3 4 lt ojl23 9 31233 39 8V2 Sr m 23 1484 K Jan 1710 24 AM Using the De nition of Derivative to Find Derivatives Jan 1711 07 AM 33 Use the de nition of derivative to nd the derivative of f x 2x2 3x 1 2 f4 3 X awh 36M Wm M Z W W h h M50 m aww l HM La 0 iim in a Jan 1710 24 AM 34 Use the de nition of derivative to nd the derivative of f x xx 1 Wm M C gt4 Jan 1710 25 AM Use the de nition of derivative to nd the 1 x 2 I derivative of f x J M Mn F f kea 4 Q HA O J W ZB 39 1i 70 le o m l L 1W 4 1 M60 V7 quot Lwm Olt39gt Jan 1710 25 AM 36 Implicit Differentiation Jan 1711 08 AM 37 Give a formula for g in terms of x and y given that x3 3xy 2y3 6 3 3 x 3 B 932 O Jan 171025AM 38 Give the slope of the normal li to the graph of x4 3xy 2y3 2y at the point 01 3 cl a 1 0 HX w M BHW 2w of o1wauk A ok o3lto1 L 7 3 X AX ok 3 A F 5 is l 2 REEL 393 ha f B 39 OHM Slowing1 M ormox l mL d 0 I5 Va Jan1r10 25AM Give an e nation for the tangent line to the graph of sinx y3yx y 2x 0 at the point 00 A yd oosgtlt 3 34 fo 22 O H 09 m rack 4 msoox 330 539 3249 0L 4 55 3 1 3 0 I 0 Mob W5 39 3 5 s 3 7lt wa pund m Jet RC UM it S y 33 lt wng 0 0 00 m cw 13003e1210 2 3450 1gt i o t7 6 0quot gt4 a a aDMCT VW 2 6 MM aimsraft 0 803 gt og a evmnCWmWNC X Aaj Ojv oo Jan 11026 AM 40 Related Rates Jan 1711 08 AM 41 A 5 foot tall girl is walk lg towards a 21 foot lamp post at the late ofl feet per second How fast is the tip ofher shadow movin when she is 4 feet om the launpposl A 39Z SLC dd 10 m was T 7quot g um 71 WW 3t shutsn 3 as I 39m wl r Mng e 7 M 39 Sr M W i vvwmi f S S Sx SQ I S MT a u mU 1ro Mc w 23 5241 lo M a Jan 11013 AM 42 A 16 foot board is leaning against a vertical wall Ifthe bottom ofthe board slides away om the wall at the rate of3 feet per second how fast is the area of the mangle formed by the board the oor and the Wall changing at the instant when the botiom of the board is 8 feet from the wall K39b L W 1 a H X om a2 EMA WW X 1 7 d H x S e xz Sasb rl x 2s 0m 019 3392 Jan 11014 AM 43 A pile of trash in the shape ofa cube is being compacted into a smaller cube Suppose the Volume is always a cube and the volume is decreasing at the rate of 3 cubic meters per minute Find the rate of change ofsuxface area of the cube at the instant that the volume is exactly 64 cubic meters Jan 1710 14 AM 44 A spherical snowball is melting in such a Way that it always retains its spherical shape The surface area of the snowball is decreasin at 111 rate of 4 ca timeters per secona Find the rate of change ofthe volume when 6 Iadius is 2 cm d vurc 37 H1 93 Z r3 t A a wk rz LCm Jan 1710 14 AM 45 Differentials Jan 1711 08 AM 46 Use differentials to approximate the following expression 31002 Jan 1710 26 AM 47 Use differentials to approximate the following expression 155 37 1 I J amp 1384375 39L 9391 U Jan 1710 26 AM 48 Use differentials to approximate the following expression 33 3 36 Lzs wu WW 3 3 3 9 35 35 333 393st 0 a m 2 439 371 20 g39 Jan 1710 26 AM 49 Use differentials to approximate the following expression c0562 92 m 3E COWJV l39 4390 radm qs 92 ga an FM Gas 4 364 39 53 34 quot501T 1 Mix MSW as 23 d Knew gig 20 Squot I Ji ilqol c J 04697700106 M w kw Us1 Ji Jan 1710 25 AM 50 Use differentials to approximate Ihe following expression sin13 H39s1r awn q aolwml 3 W n S 393 603 hms 6 all WCO I E E L LN s mL f gm Li I Z weaved m 391 erf E e 4 7 q 211 v e 2 06824240980 l m M v Jan 1710 26 AM 51 Es nultq i 4 given that15 l amlfquot39 Sxl Z s B i 4V5 lt111 73305qu Jan 1710 28 AM 52 Newton s Method Jan 1711 09 AM 53 Use 2 iterations of Newton s method to approximate a root of the function from the given guess x 39I 24 x 5 I A 2quot 3 AW 6M 5 v X2 cl 36 I S 3 5 0 Ll 39 H q m 634393979592 13 g 39 4 93 0m Jan 1710 28 AM 54 Use 2 iterations of Newton s method to approximate a root of the function from the given guess f39 quot 4x l X Z VG 37 1quot Srx m 5 1 3 cm a i 3953 1g 3 693 MW X2 7 1 31H ll cquot 1 860978520 Jan 1710 28 AM 55 Use 2 iterations of Newton s method to approximate a root of the function from the given guess x x 25 x 3 39H32 36 213 I x39LLVW quotI 3 139 1W3 v N 2324018982 Jan 1710 28 AM 56 Use 2 iterations of Newton s method to approximate a root of the function from the given guess v i 5 30 v 2 VGA g3 mm c 2 2 71 939 l3 3 6quot Llo 19 qvo N Ho 91qq03 111 1974350913 13 Jan 1710 28 AM 57

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