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M 408C-Goddard-Fall 2004-Test 1

# M 408C-Goddard-Fall 2004-Test 1 - 408C Exam 1 1 Evaluate...

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/ q'-t 408C Exam 1 Name/EID :\0 Calculators, notes, books, friends, cheating, etc. Each problem is worth 10 points. 1. Evaluate lim (x - 3 J ( fi ~ f)<.\:. 0- ~"-:,) Cfi ~ JX) x~3CV3- Vx)( f~-\- S-x') ,,-'l:) 3 ~ ~ - x lD ~ (Ji~.r)C\ -~ J?, ~ Jx. = ))-\-)3 z: -2~3> - \ -, 2 F · d li tan5x . m Im--- x~o 3xcos 2x :: ~ \$)( ~ s~ ,,-S)( L _\ L - ~, (.0'::. L. c 10 l\. --'0 ~)( f\-...• S,< K.-i O (_ID 5 \ \ f \ -w - , I - ~ ~ 3. Find dy/dx if y = 4~ + 2x 5 - ecx. - vx3 - -- - - ~ - - ----- - ---------

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4. Find dy/dx if y = jsin(x 5 ) X2 + 1 . - 5. Find dy/dx if tan(x 2 y 2) = 1 + y3. sec.?.(r ... 1 .... ,-.y>c"- 1') J I -\ J'2. 2x J ~ r""I 'Z. I J j ~ )(.'lJ l' ~~"'l.("{'l~l + AA,:)'S4'lH-/) '" 1 1 '- J' 'l '\. --z. G "t.. ~ '\ _ '/ <. I '1 'Z. I 2,-/ 1.. 1.,\. o\~J 'i>{L f\..) J - 2>'j J - LK J J ~~c.. l."'- ) ') 'U< J C "",,'2(11.'1 2 ') ~ J' ( <''j, - )>cc J S<L -z. C,,'" J >-') _ (-:. 2>C J 'Z ~e.c L LK-l. J 1.) _ . J ~~Z ~.z- 'j S<--L'Z. (-( Z '1 L) ) 6. Fmd the absolute maximum and ~'J. interval [0,4]. irumum of f(x) = 10 + 2!x - x 3 on the ~ L,,-\ ~ \-0 \"2--lK _ K). <. t 71 It ~ l'/ -\-~ -z ') 4 1.1 - ))CL -- '2-1 ,..-- '( 2 -=- ,'\ j.o; ~ 01 ~ - ~~'S W'\,\ -'" c;...\ ; (0 :.. lO ~L ") ~'l' r- ~ ( ~ );: 6 "'\
L \(L~ ),."'-\ - \l~) h-">o '" 7. Let f(x) = 3x 2 - X + 1. Use the limit definition of derivative to show that f'(x) = 6x - 1. L (b{'(~-h\'- (~\--h\'" \ - '-- --S~l.-)( \-\) \-.-10 '1\ I ""\","," _ C~~2.-)( \ '\ ~~hl..\-31...1.0- \r\tt~ .H(71 ;;- :'(K l •. z..~1,.. -\I,. I-C'( +- '" ) F \A. ~~O h ~ (,(y< -\- 1>"'-;( -\).< \--.->0 y< 8. A particle moves in the 1st Quadrant along the parabola y = x2 in such a way that its x-coordinate increases at 10 ft/sec. How fast is the angle of inclination

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