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05m1-solution

# 05m1-solution - 3A Midterm i Spring 2005 Instructor C Wei...

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Unformatted text preview: 3A Midterm i Spring 2005 Aprii 22, 05 Instructor: C} Wei \ Sch/{7m Name Discussion time (circle one): 1pm; 4pm; 5pm; 6pm Totai Scoxe: 60 Your Scores: 1. c 2“ 3. 4. 5‘ Your Total .. c . Books, notes are NOT aliowed. Continue on the back of the page if more Space is needed READ the pl'oblems oaJJequy. No calculators axe allowed 1‘ (10 pts) Let f(a:) m 3:2 —§— 3:2, ﬁnd f’ (:13) using the deﬁnition of derivative, 1324 ”WW m 3 m. “WWW Aw / [WW 1‘2{rH,/-* (KW-3x) I’ve/a A /, ,x/‘mé +41 + 3;: +34 ._, x931 :7 (m n . ' hww h =3 ﬁn A/zxwkl; +3) 1:: ﬂag (”M-+3) L164? A [who 3’0 Micimm 1 15s and of go 515%“! 01L r49. 2. (10 pts) Find the equation of the tangent line to the curve 1; = I + Sex _ 317 that is parallei to the line 3:6 + y = 1. 751's Vol/am [CM awn, H I/Mef Le fat/0M 3f tin. ”M'1X+ng \ 712,, MW»; 1;; ([9],; a; ’2X{‘j’ .3, 7.35 M=+Z ”7“ a} gsI+re"-»2x 7‘4 j": fax/.2 Kw , g; 6 7K; gymnﬁw of 7%! {’ij /fu& M 57“; t (10 33133) )Show that the equation x +1m1/a: has a solution in the interal (0,5, 1). [at (m e ”I” ”if , W ’3 “WW” 0'" {MCI} if. WM) «5 (31:) H "2 <0 4“ (20 pts) Find the following limits, if they exist. Give masons (mummiﬁi __ , JET: ”I . r»: +/ M [NH W... ~ “*3 Y’S My»: +1 V fﬂm Yip—Z “I I '"” ”'2" (b) 111nmwg 162({30835 + 3) ﬁnal-{£047}? é!) 2§£o31§7ﬁg gcf 1. 1. f0 2)( 5; X {4‘5”}? 1‘3.) 5 (FY Mow km 2K1 i>0 M4 4%1 go PM? PM? [51. 5 Mar: Mm //m )(LKMI -—— } 1’“ 2 14;, k W "”0 (d) 111m...-oo —————M 2-2—6 __// “MW/X ._.. /, WW/F/F/ 1.31M (mm/y ‘" XL.“ 2...”; --- 1/ ("'11, 7.1/14“ M : 3:400 lvi- k 5. (10 pts) Polonium—210 has a. half—life of 140 days, If a sampie stalks with a. mass of 200 mg, (a) ﬁnd the mass after 100 days; (13) when wiil the mass be reduced to 10 mg? ...
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05m1-solution - 3A Midterm i Spring 2005 Instructor C Wei...

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