Sol-165E1-F2010

Sol-165E1-F2010 - MA 165 EXAM 1 Fall 2010 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 1 Fall 2010 Page 1/4 NAME GRDEING I Page 1 / 16 STUDENT ID I Page 2 / 31 P 3 22 RECITATION INSTRUCTOR . age / Page 4 / 31 RECITATION TIME TOTAL /100 DIRECTIONS 1. Write your name, lOHdigit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one. . Write your answers in the boxes provided. 03 4. You must show sufﬁcient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators or any electronic devices may be used on this exam. 1 {79¢ -— 5:12- Write your answer in the form of interval(s). xi “x >0 @ . Find the domain of the function h(a:) : x ( 'xml‘i') :1“? C) + y AM. a7} 0 m1 m. 0 «rtmhlr ti" 4* Wgwayawnwwwsmmxgw..wm«a.My.~.mm_§,g, (3 >3? (“0(3) 9) Ll (9/00) (11) where the graph intersects the coordinate axes, and the asymptotes, if any. 2. (a) Make a rough sketch of the graph of the function y r: f : —e_m. Show clearly y 2 1 (Q +-—+ l l ﬂ —>:E (b) True or False. (Circle T or F) V x _2 (i) f is a onevto—one function. F (ii) f is an even function. 1 I; {XML T F (iii) The range of f is (—00, 0). T F (iv) The domain of f”1 is (0, 00). (v) f is increasing on (—00, MA 165 EXAM 1 Fall 2010 Name (6) 3. If f(a:) : 2:63 + 3, ﬁnd a formula for the inverse function f”1. ijféo m 3 w 2) ﬂ» :5 ti 3 w W27: %Wfi9~§:§ 3 M (8) 4. Find the exact tvalue of each expression (a) 8211,13 : 6‘2“??? ﬂ - , 10 m (b) loglo 25 + log10 4 : Mﬁmﬁgge) beam 0 W. g; 5 (c) sinf— : N We 1 (6) 5. Find all values Ofx in the interval [0: 277] that satisfy the equation 2 cos m+sin 2x = 0. aces}: en ‘2 sim mm; \$11; @ £535“)? (item; Q :r Q 33mg 2:? “Ll (4) 6. If a ball is thrown straight up into the air with a velocity of 50 ft/sec, its height in feet after 25 seconds is given by y = 501; — 16t2. Find the velocity when t = 3. (v {a .3; 5‘5 might: mm «u ("'23) 6% “ﬂ: “ilk! *1- (7) 7. Circle the interval in which you are sure that the equation :34 + 41: — 25 z 0 has a solution. State the name of the theorem you are using. Le); {(24) “27%Aigﬁﬁﬁa @253 £64) ammunth Ulnar nit-w [0,1] , gm) @2553 agent”? 1.??? 13%}?! [1, 2] / €41) we?) «<0 W1 git) W [3 H my :21) gt?) is at m, f , [3, 4] F , Veg 1, m M 1. nxﬁ‘i’w, '( Theorem: :[Vklllgf‘ﬁhﬂliﬁﬂ tr ugh; i h 47% i M l l MA 165 EXAM 1 Fall 2010 Name Page 3 / 4 l (10) 8. For each of the following, ﬁll in the boxes below With a ﬁnite number, or one of the symbols +00, —00, or DNE (does not exist). It is not necessary to give reasons for your answers. a l + l iii; , , g W m k (a) 4 m 2 RM“ 7— ‘1’” :rﬁilww m m—>—4 (6) (6) 4 + J: 2‘9 “,5 t. 67% X»? 4 ﬁ/ﬁ; “4?; W E 1 m 373 X r w {W , , 2 — 5L” ~ 2 (b) 53% (a: — in k-_/’ a“? 4 hZ—l l6+gi'1%l1"§é (C) 11m .<_+_>___§ : W hao h law) 0 h (LAW) 2‘; MW {13‘} iii :7" (3 (a l? Vb f} l“; if, 2 — . o (d) lim I“ = m maﬁa m——>-—2 )4 Ln meow r52 ,2 >1, 4:0 3. x Wath 'L “if”? 1 l ‘_ l 1 3 l ‘ i (e) lim — — ———— = 2”" ' z~—>0 :1: 11:2 —|— 35E Z>f WM? ‘ "L, f ‘ . ,(‘l‘ we” yaw S‘ 4 g” 1% :5; hf} ’j::a;7w.i..\$);0 “:90 ﬁt " 3’ i w”“"* 9. Write the equations of the vertical and horizontal asymptotes, if any, of the graph of \ Vertical asymptotes x ‘ff: {L , ’7“? it, i ‘3 Horizontal asymptotes i W z r (b i. n 2 * , ,, 1‘ x: x ,» , 'i Le “x Y siggrwsugw 5473mm mm :1 mm- r 2 x —:1: . 10. Consider the function f = x2 — 1 If m 75 1 , Where A is a constant. A I if a: = 1 Find the value of A for which f is continuous at m = 1. O pf Filmillgfﬂw“ no l iheiu'eoﬁi‘énﬁi like Wﬁ‘lgl“ l ‘92,. . ‘ L“ _ f}, _, x i \D twru‘iVatican it, " MA 165 EXAM 1 Fall 2010 Name Page 4/4 (10) 11. Find the derivative of the function f(a:) = x3 + as using the deﬁnition of the derivative h _ f ’(m) : [lir% (0 credit for using a formula for the derivative). .% /‘ f E ‘ :3 I [5" 3.3%, Q gm :3» QM hm (“M-h) (a?) law?!) it \h who W’WMMiV/mmr ix. 9 ‘ 'E r ’3' 3 .l, m {cling ‘ m “FEX I? .3, . Winning“- he» 0 Z M Z (I ("(3 X + 334% l if Wm mm“, M What“) in ? h am ,(3><Z+?>M~ award) ltwiio H @ “agar/{it (6) 12. Find the equation of the tangent line to the curve 3/ = 1 — x3 at the point (0,1). Ola (15) 13. Find the derivatives of the following functions. Do not simplify. : 5') “ﬁn final/2 Mi 5: (a) y SinfL'. at» (M. m {SH/W3! a xeow “am (b) = ﬂ tanx. sec 6 6 = —. (C) M ) 1 + sec 0 Erma mgﬁctst’rt) lava ' ...
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Sol-165E1-F2010 - MA 165 EXAM 1 Fall 2010 Page 1/4 NAME...

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