Test1aSoln - MATH 1501 D1-D4 Test #1 Full Name (Print) Page...

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Unformatted text preview: MATH 1501 D1-D4 Test #1 Full Name (Print) Page 1 of 5 Version B January 30, 2008 Circle your TA’s name: Cindy Phillips Maximilian Hertanto Blackili Milhose Michael Rothberg 1. Evaluate the following limits. If a limit does not exist, write “DNE” and justifl your answer. D0 n_0t use the L’Hépital’s ruler i . (21) 1mg r W X f x ‘x-‘ wz me) . i w 3‘: gm _ w view" :. A. (7pm.) 0 X?1 X‘l'l 421—3 3 lim —x_2 = J- x->2 xz—x—Z 3 (b) lim Sink . : “5 a) {X x40 s1n4x 'X 3,0 - ' : e W. M 35> x $35? '3}: g Mfigfi 4%?“ (7 pts.) 1 y w. - X em 3 96 “Mg M 1imsin3x ’Hflsin4x (C) P2} f(x>=where f(x)=l2:: l jflfimgcx‘3bfivfi WM Xvi “' _ (7pm.) , #927??? :3; £44?) l g. ‘ Kw l x w; l + lim f(x) = xahl MATH 1501 D1__—D4 Test #1 Full Name K a I (Prim) Page 2 0f 5 . Version B January 30, 2008 Circle your TA’s name: Cindy Phillips Maximilian Hertanto Blackili Milhose Michael Rothberg 2. Givean 8,6 proof for final—5x244. \ R m ,7 Mn w a: m m M a M i {gem-336$ '-j&“ imgx nmi% 3. ga) Explain the difference between the removable and nonremovable discontinuities. Iii am is we at, a; WWW gee aegis fin (5.2; J‘E‘mzfiwfiwvé‘xfi‘ Li» 2536 - malammamwsmzwammm “$in € S Gm£il Warm. '. C. _« z ._ _ . . =‘ . ve an ex’zgmpiegfa Jump discontlnuity. , 1 1 a £4; 4 J? (K ) «fl {5+ ‘iBiQifi-wg / g we 53% M41 Ame»??? i’ 3" ‘ {:th ls) We 3‘9: {I MIL/LA. gain a? 3’4“: h é ‘ V5 MATH 1501 D1-D4 Test #1 Full Name K Q t (Print) Page 3 of 5 Version B January 30, 2008 Circle your TA’s name: Cindy Phillips Maximilian Hertanto Blackili Milhose Michael Rothberg 4. Determine whether the each statement is true or false. Justify your answer. (a) If lim7 f (x) does not exist, then f is not continuous at x = 2. xwaw I P h , I W WWW (b) If f is continuous everywhere, then f is differentiable everywhere. (6 pts.) Circle: TRUE 5. Let f (x) = x2 + 5x. Use the limit definition of the derivative (the limit of the difference irrii“i&;rt°gc.fi?d5é§: a a m rm {Emma flaw-99*(W - - . We & r? a - ‘ _ ;.. :s: Q *- év is? is" (10 pts.) :1 Ed: +€AR w it “6" “WWW MATH 1501 D1-D4 Test #1 Full Name 3 ' (Prim) Page 4 of 5 Version B ' January 30, 2008 Circle your TA’s name: Cindy Phillips Maximilian Hertanto Blackili Milhose Michael Rothberg 6. Evaluate the following derivatives. You do n_ot have to simplify the answers completely. (a) %(3—3x2+2x—1) =- SXEG" 6% +2 (8 pts.) £03 —3x2 +2x—l)= d2x+5 w. a J a 3—x saw) ~(éa-XWWMD? .‘?"n#"~‘°i5-i~"‘-‘W< “'95 “ties-w“ Emawmamwmgmfismix:#:m-fi‘N'ewfi-flflmssiimx’ou‘i "'1'21‘" 5: {smsi% (8 pts.) Wfl-deflfl'ufiw7w an"; d£2x+5j= .2, m «~— ‘32 its? (vi) — 3—x m . 1. r q, .fiwm-‘u-flifiqw .--- -. - maxi-new - 7-'Meflummwmsssnmflmm "-ln-Afimiflsulmifi' dx (0) _ gait—4| (Hint: Write l2x—4l as apiecewise function.) :1)! ~ HL / X Z a ~(2..x-‘+)/ X< 2 {RX-Ad : MATH 1501 D1-D4 Test #1 Full Name K g j fl’rinfl Page 5 of 5 Version B January 30, 2008 Circle your TA’s name: Cindy Phillips Maximilian Hertanto Blackili Milhose Michael Rothberg 1 7. (a) Find the equation foratangent line of f (x): atx= 1. / F/ 2x—3 (X7 - __ {ear-31) M a / (axawi (abet mtmzwa :3 Qw-ef' (10pm) T I : _ l 2-1 "5 1 (b) Find the point(s) where the tangent line to f (x) = is horizontal. If there are no 2x —~ 3 horizontal tangent lines, write “NONE” and justifl your answer. (/i Q h x Qfiafl * E» « '(4ptS-) ' Point(s) with the horizontal tangent: N ...
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This note was uploaded on 08/12/2008 for the course MATH 1501 taught by Professor N/a during the Spring '08 term at Georgia Institute of Technology.

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Test1aSoln - MATH 1501 D1-D4 Test #1 Full Name (Print) Page...

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