M408C Exam 2 - du )( M 4030 Exam 2 Reid Fall 98 ® .051:...

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Unformatted text preview: du )( M 4030 Exam 2 Reid Fall 98 ® .051: 22:. on» }. 1. (a) Let y x: W, m: z (31: +4)”. Find g; when m 2 —1. f‘“~(éu)(2‘u)-(»m{suas) zzmuugum: W33“, 9 Ed"; ‘ (2'0): ii'u)‘ 9L3: (ELIA‘36d1'53 ~ {:2 (2.?) 43* 2-9 liq 0“ 2%)): {-3 w)‘ 1 3' ’ 'C’ "8" Ti (b) Compute the derivative of: flat) : <5:an)? (You do not; have to simplify your answer) I L Fwy (JV 1%" 5:2 MW m ZMWME 9 W 1 I‘f“ K3J3 2. Consider the curve 33 —- 2xy+ 63,? = 24 E/ (a) Show the point (2,?) lies on the curve. x"?- . ‘1 " Z 1.. Ca"— mmrw cw ' 2" a? * z w 2% "w 2" ’6 Zq‘: Z q f :1 (LAst 091 f (b) Find the Equations of the tangent line and normal line to the curve at (2, 2). m; I. Y » Zxou, g: (254‘, j g "at; a5, 0 d3" arm m 26 J, 5332 7 313» C3} d1" 23*13} 0% _ 3&3“ Dix 24% - 12(1) (2: ,. 3 Q _ £73 7 (TIME? 1 ’ 1&thfi‘p7 firmi‘sw/f 0’ :1; i - _l 7- ’3 * Nam; {Jam “If! 3. A rocket rising vertically is tracked by a radar station 6 miles from the launchpad. How fast is the rocket rising when it is 3 miles high and the distance from the radar station is increasing at a rate of 1580 miles per hour. ol {Smog fig.“ lgoo M; Q“: 1 1 ‘2 ~ tack .. zeta .Q 1 A at .5 Z a?) ,, (m) Jag: 0"» 435‘ :33. a vital 2 m oh: ' 2k ow :W<SJ“‘?“ 4. A particle moves along the x—axis with position at time t 3 0 given by 33(3) = t3 wfitz -— 151:: At which times is the particle at rest. On which intervals is. the particle moving to the right? {hfi wt, fife”? hH‘vt-‘w 11({1‘} '1) O XiK-H; 31" ~ {21‘ [33’ : gag“ — 5):. gaéflfi) :0 AT $530 W "LH‘O 3/5 Questions 5 and 8 below refer to the function :$3+15 bNE 1k? 0/ 7» I" fix} 5.(a) Find the i1‘1tervals on which f is increasing and thme on which it is decreasing. E ‘ " '2, ) 3 - 3 .. (L. 3, 1 ,_, 4 '- ‘K '2, 1 (1 WA ‘* Bx (flag {4‘}, ngTH? x ‘ W x " 2. K 3, m =2:- ng‘fé Q ~ tx‘q’t. :3 Z5): {Cu 3:» x »8 33> X Z (b) Dermine the critical points of f, and the nature of any Iccal extrema. pm m— om: k? 0 5m x _ ‘ x:’Z 42-42) [aHim magi/l US 6(a) Find the intervals on which f is concave up/down and any inflection points. 3113‘ 23:374.! 5% ” My“) X ‘ x : QYw_[/{xw+ 32X 213432 4.; 1K.) X“ ‘ k3 ‘ X3 0 to m x’wwco, K3245: $7.7: : ‘35' 3M * 1 3:: \/ Cog/cilng U10 3' (fog, 3Wlé0, *c’c‘) ffiNC-AUI; 913W” ' O) IbFLECn-ov FG'MZ’; ‘g: 3W ’ (b) Describe any horizontal or vertical asymptotes, x and y-intercepts and then sketch the graph clearly marking the information on the graph. ' ,Uo Hsfim zmmm M w n are VfflthfiL fingflfarf frfr kdrO‘ (Mg m; mot-r W0 ‘1~IA'1"(/‘cvffl4 Xflwfifficgfl'r 1 if 49.x, 5/5 ...
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This note was uploaded on 02/09/2010 for the course M 408d taught by Professor Sadler during the Fall '07 term at University of Texas.

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M408C Exam 2 - du )( M 4030 Exam 2 Reid Fall 98 ® .051:...

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