Key Test 2 f'08

# Key Test 2 f'08 - u='v-u Horizontal asymptote(s-l Vertical...

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110 points Math 111 PIe dge d,_-=-+ _ 1. Water runs into a conical tank at the rate of 51f ft 3 /min. The tank stands vertex down and has a height of 10 feet and a base radius of 5 feet. How fast is the water level rising when the water is 4 feet deep? V = 1l r 2 h (16 points) ~S' 3 l' d V c .-- f*· 5 J l "Clt \ I \ I t,\ \ /-; := .::J I 0 I JJl -? LIt I\j,. ,/ .. --t\ ::. l../ ~) ,=- ';] i-t- if -, :/1 J- c.--- J ..L \ ()- 0.../1- _..L -::: .:? - ') '\ -= d...Y'\ _ - ----- '-\--' I 0 ~d Jo _I L - ~~ -~~ V ce ¥ r ~ '--- C:ili- -;>,~ ~ 0i ~ l!- f \' 2 M -T- ;;J'\r;!-A J"\ » STice F'-1 c!b + d~~l ('fJ d~t 3 L Ok cU.- J 3 l cL-c ---~-}. ~-----

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page 3 3 c) lim 4 - x :=: _ J.. x-H«>3x 3 +x-4 '3 ) XL. J +00 X2- __ 78 ) · x e 1 Im_ Do X~-I+ X + 1 :::: - l~ ~ \,; c.P: b D -\ t) l~ sec 2 x ::::.. -+ 00 x~_ 2

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page 4 2 5. Given: y = - X 2' Sketch the graph and give the following information: (x-4) (24 points) Use the next page for any calculations you need to do. Q X - \ ltJ C;< -\-~ J y'= _~(-I'."t. L1~)-,--3_____ y"= __ ........ _ (-I-X~-_L\ .... :...J..L..'1

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Unformatted text preview: u=-) 'v-u Horizontal asymptote(s)----l Vertical asymptote(s)~ Point(s) where the tangent line is horizontal._. ...;;.{_0-i-J-=O--'-) _ Interval(s) of increase __---'-X __ <_· _O---e.I_'_X_>_Y C-~)-~) Point(s) of inflection '-----,O---'''''-'-''----,f-+------2 Intervals of upward concavity X L _ Maxima to) 0) (if appropriate) Minima tv an e.. (if appropriate) Sketch: (Clearly mark all important aspects.) t1tJ-I I I l;c~t-\ I ~I ljO=-~ , ~-7 ( ) I page 5 ',,. , page 6 6. Given: y = x%' (x -4)2. Sketch the graph and ~ve the following information: (20 points) DO NOT FIND CONcA VlrY: ~()(-L/) (X-I) y'= .3 X '/3 3; . . Point(s) where the tangent line is horizontal ( 4J 0) ·. ('11 9) ,.';"\ 1,. . (0)0) ~ ... Point(s) whe're the tangent line iS'vertical > Intervals of increase 0 <. X L. 1/ X"7~ /Y Maxima (I ) q ') (if appropriate) Minima to; 0) (4t 0) (if app~riate) / fA LA. ... 2 I,' (J (fl AX . 1..J-IT, (IJ 9)...
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