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# Exam 1 Study Guide MATH127

UMass

GPA 3.2

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## Popular in Calculus for Life and Social Problems I

## Popular in Mathematics (M)

This 2 page Study Guide was uploaded by Elena Bassin on Thursday February 26, 2015. The Study Guide belongs to MATH127 at University of Massachusetts taught by Adena Calden in Spring2015. Since its upload, it has received 71 views. For similar materials see Calculus for Life and Social Problems I in Mathematics (M) at University of Massachusetts.

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Date Created: 02/26/15

i 1 REVIEW SHEET 39 i i 1 Exam 1 Review I Pe odicFunctionszyAsinBtC or y AcosBtC a Amplitude IAI max min I 2 holfthe di 39erenee benveen its mar amp min values 1 Period 21 I Bl time for the mcrion to execute one complete cycle i 3 belongs in the EQUATION Period is the value you see on the GRAPH c Vertical shift C max min I 2 the disranee om the midline to x axis 1 Word problem 1 Sketch out the graph using the infoi39mation given 2quot Solve for A B C 3 Decide whether it is sine or cosine 9 construct equation Sin parent graph Sin graph Cosine parent Graph N 1 3 l 2quot an 1H 11 Average Rate of change slope of tlie secant line slope betweenavo points 3 III Average rate nd the rate of change r re 4a I n f IV Interpretation of the Derivative J a InstantaneousRate of change slope of the 1 tangent line we are int rested at what is happening at cite point i SAME formula as average rate of change but use vallie to the q and right of ppint given fb fa b a b Lahel points on the graph to the right 1 393 0 J f xs 3990 r f x 1 393 0 V Linear Approximation do NOTiuse calculator it is an approximation 3 fnew 1 old F Pdldnew old VI Limits a De nition of the Derivative plug in at into the de nition of the derivative u L 1i fxhfx l e 1 4 m H h h 39 5 Tat i 11 b Functions are continuous wherever they ai39e de ned Polynomials 39 Rational Functions What is not tiE nqdl a 39 Power functions hue functions 39 Trigonometric Functions iquot Exponential functions in the form of orquot a gt 0 a a 1 Ti 1 n F 1 functions of theiform logax o 3gt 0 eat 1 39cT Hon to solve are A g r a a i i Esthhai the lin t quot do NOLF i15e calculator use the table by testing smaller and smaller values getting closer to h a 339 i Solve for Hm 9 filug ihto calculator multiple choice answers w decimals should indicate to you use calculator ii atom 9 fa tor the limit and solve a e s i VII Second Derivative f lx 393 r I 1 39 v i i a Rate of rate of change looking atthe slepe of slope when grapli39inglooking at concavity on a mction when graphing WEIEmil 39 J t r 3 t r 139 T q r if I b x 9 f x N I 393 10gt 0 on an interval then fx is increasing on that interval J Wm 3 lIf f xilt 0 on an interval then x is decreasing on that interval quotquotIffquotx E 0 on an then x is constant on that interval o x 9 f jG 1 W j 0 X 1 on an interval then f x is increasing on that interval gm lt a on ah interval then f x is a ir asin gquot 8i claimant 39 1 1 Iftquot x m 0 on an interval then Px is constant on that interval i d 1t asf rate of rate of change Wconcavity and it VIII Relationships between fix f x fquotx th 191 x 1 00 100 argy x x 9 f x ff 1 i t ji39la 5 Leela m El i NW 3quot Wrath 11 IX Derivative F orniulas x 1 Find t x given for 3 I 1 I l E a a g gel s 39 Fjasx i4 5 5 i y 1 3 F t J I I H Fi WK 739 amp1 i339 quot i5 v b 39i if i 1 quota 67 iii i 12 Fingl anngarivn ofy i4e lnx can 64 3395 II 39 quot m o 39i g b Min titan J contam Em quot1 42 Y L E L Aquot H9 51 03quot 90quot U3 39 ii 50 Hquot Ki 3 Find j x 23in i 6cosx 1nx 4x 2 23 vi l lngobt i 61 Yi hca 4 if 39 i f i xi 3 139 5 a a 394 D 1 39 i in Types of Problems 1aknrq 3 1i 5quot g 3 5 I39 What is a function f 1 1 i J r F g i Average rate of Change quot 39 39 39 i 39 New Jnctions from old 1 34 Find the slope tangent line to the graph of fx 3e 2quot 39 6 at o Camposites know how to solve algebraically the poimizma W hen x 1 0 graphically and ora a table 52 3 210 o 39 Periodic function M i finial 43 1m 2 39 2 i 39 0 Given 399 So equot 39 quot Equations gt 39A a c t 3 RW ben i 5 i 33ch ELQt i 39 Word problems 9 equation z b 25 quot to q I Graph equation i q I Table 9 equation t I 543 i Instantaneous rate of change 1 gt5 i wquot Y I 0 Give We ndfbest Estim tc 01 x quotTlii iina E quot Unnd 3901 TANiiENT LINE 4 I Use ecuatiom use values to the left and right of value I F d f th d i 1 0 MEREl Appmxhn om H n r 1 a 1n x e eqyatlve represents the sgpeof q Word problems irate at change f x the tangentchne 39 Derivative function GRAPIHNG 2asubslitltte x 3 mintokfxn 399 slope quot Interpretations 0f the derivative 339 Substitute x n T The Wand derivative i 39 W c Tablas Gmphingg om Problems Algebraic 4 Substitute x y mmto y solve forb 1 Limits andwn nuity 5 Plug 11 m b Get equation I i I 39 a i 3 o What is chutinuous What is not P quot I x 0 Estimate nd values approaching 11 i i quotHquot 5 I i i WO DS 0 De nition of the derivative which of the folloWingrepresents the 5 39 quot r de nition of derivativequot i a i in n i 39 i fix Emmiquot lW f 1 if 539 339 1 0 0H 399 f x a Rate of change Litinstantaneous rate of 39J In 1 v J a Derivauve Formulas n a at I change derivative slope at one pcmt gt o Derivatives how to solve algebraicalrlvI l Rewriie 2146 a i r tanggm linge yfo velocity 2 933 g f gt 11 0quot n 39 i n r fa Rate of rate of change is the rate fine i39 in quot3 33m ti increasingfdming Slope Of he 53003 N acceleration

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