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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~
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,y,’ w 6 ~—._ #4 (6+6pt) (a) Suppose that 4 cos2 x — 4 cos x + 1 = 0. Find the value of cos 2x. .L
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(b) Let f (x) = Calculate the inverse function, f ‘1(x).
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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»
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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
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I) sin(492) (b) Evaluate the hmlt. 133(1) siM392) 3m #591 . : Hm wMWWWm {32%;} 1’ \ m 4 Q #7 (6+6pt)
(a) Find the horizontal asymptote(s) of f (x) = 761%sz I? _ x3 —4x2 +5 ——2x3 +10x+11. (Show a proper amount of work) ‘\\Wﬁ\‘ w. r. J M:
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/ 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...,
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‘im it a wivémm‘mﬁ UCW‘WW WM} (433 (‘mt‘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..
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 Spring '08
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