Calc1 s01 midFinal ans - #0(lpt Please write your name MUST...

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Unformatted text preview: #0 (lpt) Please write your name. MUST TYPE. #1 (3pt X 5) True or False. Do NOT explain. (a) ln(—1) = 0. 1% 3r; (b) For positive real numbers ln(xl - x2) = In x1 + In x2. (3. (e) Iff’(2) exists, then lirzn f(x) = 1m; fix) x——> — x—> #2 (4+4+4pt) The graph of function y = f (x) is given as following. y (a) Based on the above graph, calculate Iii”?+ f (x) if it exists. Do NOT explain. 30—) ,3”: 2‘3..- (b) Based on the above graph, calculate ling 2 f (x) if it exists. Do NOT explain. 35—) (c) Based on the above graph, calculate lirgr ( f (x) + f (2)) if it exists. Do NOT explain. x—) 3 l #(0+1) #2 #3 l #4 y #5 #7 #7 #8 Total ’ /16 /12 /12 I HZ! /12 /12 /12 /12 /100 #3 (6+6pt) (a) Suppose that a"1 = 3 and axz = 2. Calculate a2x1+x2. 2 a (b) Evaluate 1n ( e 7% -+ ’Xl. W~ .- 7/361/2 eZ 9‘ J; 4..., . a ), Where e is the base oflnx. a; '7’3 a me, fir! ~ a W / ll J'V" ‘4" l L? a) ' r”; ,y,’ w 6 ~—._ #4 (6+6pt) (a) Suppose that 4 cos2 x — 4 cos x + 1 = 0. Find the value of cos 2x. .L (237 mg ‘X M1.) 3: '0 3 ‘flmifi.eaawfi j 2 (b) Let f (x) = Calculate the inverse function, f ‘1(x). 3k3¥3~r§ t W” / W '2 w "’“r- > ‘1 1“ H “x ~‘h ’ I "-j 3 }\ '" I . - V, f i ( x ‘; A» I ‘1 X y“ ’ I V __ V" (a , ' ‘ J.- i “w .w" u n/ W H p" w i ? (I: f 45 6'“ ~ j ,I , ,J A x WV ‘- «L7 m“ ‘ “e. I If x. I!" 1 1 u. 1” W i ‘X. , e - a #5 (6+6pt) (a) Calculate the limit. l {M WM, T. (b) Calculate the limit lim x—>2 75; 5 “x, x2—6x+8 x2_ 4 \ (%9~4>{X—23 hm A» Ix—al ( w, w~>~ManMWysW‘WVVm-n- %1ervz) _ ‘w (5m - a . .fi 1 z A a Vx2+3—2 lim 2 x—>1 x ‘1 3'» . ,1 «~14; #6 (6+6pt) (a) Calculate lim M 95—90 3x cl ‘3 I) sin(492) (b) Evaluate the hmlt. 133(1) siM392) 3m #591 . : Hm wMWW-Wm {32%;} 1’ \ m 4 Q #7 (6+6pt) (a) Find the horizontal asymptote(s) of f (x) = 761%sz I? _ x3 —4-x2 +5 ——-2x3 +10x+11. (Show a proper amount of work) ‘\\Wfi\‘ w. r. J M: Wm axiflox’rii - , b 55 L? :: [Hm I X u i (X 9 5+ 12 ii S» 79 x3 I, i < (‘ x .. .m‘. Emma/H“ 1AM jag." / Kwa‘C’O 5 (b) Using the Intermediate Value Theorem show that there exists a number 6 in [0, 1] such that C4 + 3c2 — 2 = 0. ’ ‘2 g . 1..., Lg+ {-00 W -§L/mC-t's’m oatmeal v/d jOO': 9< 1* 92X 5’3! V "Mi ‘im it a wivémm‘mfi UCW‘WW WM} (433 (‘m-t‘fiéVU’W/‘S W 0’ E ’ {4: _..L i " Mote H‘W‘i“ ’PO 2"" “2,. $ 0 S 79.4". Thw ‘rag flue, :VT 3 ‘H‘LCVG 1‘7 C 9 L0,; 57 iii/mm #8 (6+6pt) (a) Differentiate f(x) = 36—13- + «E + 35 (N 'a 1" "{1- Jm w} warm: 9< +x< ; {e / " fl fzx) : *%9< +3” (b) Calculate the tangent line equation of y = 3\/56_ at x = 1. , v»! 52.. V f” 3 ( ' / v 3, X a“ 3b, m, 9 w 4‘» jv. 2 __..._._—.~ "25 h l } ‘F‘ “m “WI; 04:; WWW»: A“! Pfig V / a: if? 2,, ...
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