Exam 1 Questions with Answers - Analytic Geometry and Calculus 1 | MATH 1300, Exams of Analytical Geometry and Calculus

Download Exam 1 Questions with Answers - Analytic Geometry and Calculus 1 | MATH 1300 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! L. (4points each) Match each function with the comect graph. (Note that there are moze grephs than functions.) | — CONG) Graph: D COMMON Facrals| 1-2) (4+) IN MUMERATOL | AWD DE Medd tudrah LEAD Td tro LES | ° | Graph A GRA APH | IN THE Graph; mAtcHING F IW THE hud Graph © Craph D 2. (3 points each) Using the graphs below, evaluate each of the following expressions or answer the question, When you answer the two questions, (d) and (q) below, state your reusoning. A 1 ‘ : @) 2 (2) 1f-—— —_ meee Ei if ae 1 Graph of g (A) Is f(x) continnous at x= 1? Explain your answer. YES , | dy 6 (x) oe (1) TN Fadtiae ¢ C80) DRaw GRAPH THRU (1,2) ee es Dyn $09 = fe fal oo =e) ae) (e) Lim g(x) For gv) = ta= fe ftv) isan Roa (0 ge 5(3 ) i. (x) Does 9(x) have an inverse function? Explain your answer. No, 4 Ge) FAILS =- ~~ jp Hebeow Tac tHe TE = — f a So oe) [S ALT [-/ os | Se Ste) Dops Aer Have Aw EMVEASE, 7 (5 PossBLe To DRAW A HoRZ CWE THar CUTS THE GRAPPA OF 9 IN Hate Tha ONE PLACE 5. (4 points each) Evaluate cach of the following limits, If a limit does not exist, specify whether the limit equals 20, —09, or ey donot at (in which case, write DNE). Sufficient work mnst be shown. ‘= (a) jim 2 ea a Ratio OF LEADING COEFFiClEWTS, when) dog (yuu) = dag (DE von) , TECHMAUE OF COMSUCATES ee w]e tt) hot ie - ee Ur Fe og X~4 oC fe #2 = 242 =(4] ee Warr tea =! a caby (= Get = = am et oe I= Sut x a the G ven (+e ) ROM, I-9MK ye [Suny Z Pr de (amed\= i-eat, =P aya! Katy, ) = (2) @ my sfFeoo) AS oe 4 TAKES ON VALUES LESS THAME Bue ach+ AS a1 9, Awd fh THESp # It >o Aw (-F>0, 4 -1 bh [Bsa3t\ . 2 3 he (= sin(3¢) eh oe he | Sun3t- te eo / i 6. (5 points) Use the Squeezing Theorem tu cvaluate Uhe following limit. Sufficient work must he shown L aim, = cos(x) +| = car =| fn aff x aie al zi fi MuctiPLy Taka BY p pseRve 2 x= xe os XK 76 FoR Xp +0u Y dik s)= 0” and bm (4) =0 here Ko oe sot Ss Aas x =o BY HE Seubbawe THe, koe 7. (6 pints) Using the limit definition of the slope of the tangent line (which is denoted may in the book), find the slope of the tangent line to 2, at the point where x = 2 slope of the tang: y = 2? +2, at the point Se C(2#i jt i. J~ p— ple ee m ve den Ct Hg = bac. ae 2 : oe | h >0 ho h fie tap een eI-L -foy2) 5 me Pi ea hey ho ig Sh ta, : (rh) = uh) = [FE] be aha fe aa LH ee Leer aon Ay USING THE OTHER FePmuc, ’ == (Sle = R FaQmucdreay Fok ie or May ot CLe My.) eae €fx)-Lf2) oH Ply, "phy Le he a kop Ree Se LeeLee 2) fh. Kino fe ey MP2. hoor re Ke he ge ae es = bec. (c42) = 242 =(7] far “yes for 8. (3 points each) A 20 foot ladder is leaning against a wall with its base 2 feet from the wall. The bottom of the ladder begins to slide away from the wall at 2 feet per second. (a) After how many seconds is the angle that the base of the ladder makes with the ground equal to 60° = 7/3? \ GaSe roth => ow oat 2 hug 20 2 5 Se, X =/og4 Ket TRE OSE TEAS Te SLE Ste a 2he = 7 fo Flom (TS INITIAL Posi po UTIL THE BAs& (S fo fo LUG. AT atte | THS SLibiWwG wie TARE SLA _ cus 2k, =|] (b) After how many seconds does the top of the ladder reach the ground? The Toh OF THE LADDER REACHES THE GPouwp METER THE Base sues Jolp- 2ft=B LF Ar WHICH TIME BELAD DER 1S : AWD LYWG OW THE & hou) THE BASE Ea@uAts Tye CEV GT H OF THE CADD ER An aM Tus Supe wie tave If _ | Phe THIS SUDIMC wie THE ay 1)