101-2005&2006-3-M20-July2006

101-2005&2006-3-M20-July2006 - if any. d) Sketch...

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Kuwait University Math. Camp. Sci. Dept. Math 101 Second Exam July 17, 2006 Time: 90 min. Calculators and Mobile Phones are not allowed. 1. Use differentials to approximate: sin (29° ). (3 Points) 2. Find the equation of the normal line to the curve: tan(xy) + vx + y = 1 at x = O. (4 Points) 3. A plate in a shape of a disk is heated. If the area A of the plate (in cm2) after time t (in hours) is given by A = Jt2 + 3t + 6, find the rate at which the radius of the plate is changing after two hours. (4 Points) 4. a) State the Mean Value Theorem. (1 Point) b) Let f be a function such that f'Cx) < k, "Ix, with f(O) = 3 and f(3) = 6. Find all possible values of k for such function to exist. (3 Points) 3-x x-5 2(7-x) 5. Let f(x) = I ,\<)' and given that j'(x) = I ,\'1 and fl/(x) = .... a) Find the vertical and horizontal asymptotes for the graph of J, if any. b) Find the intervals on which the graph of f is increasing and the intervals on which the graph vf f is decreasing. Find the local extrema of f, if any. c) Find the intervals on which the graph of f is concave upward and the intervals on which the graph of f is concave downward. Find the points of inflection,
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Unformatted text preview: if any. d) Sketch the graph of f. e) Find the maximum and minimum values of f on [2,4]. (10 Points) 9 f.-I I i1 C 2 L ~ ,r-f r-I 'D I .J Q \ ~ J +-.-,---T ~ /'-\j n--~~+~ ,;-s ~ II . \ f ~ y ~ L--.c (\ . ~ Ai ~ ~ \'~ J ~) C\ 1+ Jl~~; 2 '3 +-)1 ) _-r-o /'.\. y y---J! &quot;' '1. 5 ~ :r-:; ~ 1~ .~ j r-,,&lt;J / ~ ;: .:) j (j'-;1 &lt;n . .J ! 1 ' y r---:;;:-~'--\--'---&quot; '-&quot; /'-._ .J' C'--~ .&quot;7' '. J . , &quot; /&quot;-. . v ~\ \ \ \ ), ~-&quot;-j2 \- ¥ 1-1 ' I-. J' i&quot; .r &quot;,-&lt;---l ~ 'r ~ ~ , ,I &quot;'-II II ~-j&lt;J =J~ I .,-l 11 \1-:&gt;-7 ,\--:; r-~ &quot;-~ ::r r-' &lt;C\--./ 'J-&quot; J! ~------l' .,--+-'---r' + % \ 11 10\ ·-1 II ...... , A I \J\ I .r 'I II-&lt;!. f\ II n ,r 1&quot; ...Y d . . . &quot; . .. ~ J .;-.J' r&quot;-r ... .:::J-l. ...l II f\ (I II I :l\) f\ 1\ ,I o , ~ o ~ II r'l , /&quot;0-JJ _II .};)\ ::&gt;V &quot; &quot; r;:; ;-&quot;-....J-l. .l + /&quot;-J-50 )I.-+-:fO J ~ x .J &quot;'J j )1 J + o .-&lt;i-..J &lt; ill 1&quot;1 ' '&quot; ..• C:, rn I ...-j.J II /-:; /::'I=' ..J L-';I.J-t-j.J...
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101-2005&amp;amp;2006-3-M20-July2006 - if any. d) Sketch...

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