APPM 1235 Midterm: appm1235spring2015exam2_sol_0
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3 43 g- (b)%%express%y%as%a%function%of%x:%% log y 2 = log(x +1) log x % logysloglxthtlogl0o-logx-1oga@2ktb85lo8f00hxxtd. y. = 1004 +1 x (c)%%simplify:%% loga( a) (d)%%find%the%value%of% log3 4 log4 5 log5 9 . %%hint:%%think%common%base. % (e)%%true%or%false:%%a%polynomial%of%degree%4%can%have%exactly%one%maximum%value%and%one%minimum%value. % hey . egf . enuof. 2 (f)%%which%of%the%following%graphs%shows%how%the%rational%function% q(x) = x 2(x 1) x(x +1)2 %behaves%as%x%approaches%0?% 2. %%[20%points]%%a%professor%gets%a%fresh%cup%of%coffee%at%8%am. %%in%the%equation%below,%t%represents%the%time%in%minutes% since%8%am,%and%f%represents%the%temperature%of%the%coffee%in% f:% t = 20 ln(f 30) ln(140) (a)%%find%the%initial%temperature%of%the%coffee. % (b)%%when%will%the%coffee%be%100% f?%%use% ln 0. 5 = 0. 7 %to%obtain%an%approximate%numerical%value%for%your%answer. % (c)%%solve%the%equation%for%the%temperature%f%of%the%coffee. % (d)%%what%temperature%will%the%coffee%approach%as%time%goes%on?% lm ( f - 3o)=lm( 140) (cid:15482) f- 30=140 ( 3gd= - 20 70 ) t= -20 [ in ( no. 20 [ en ( 140 ) ] ( f - 30 ) X 4 2 x 3 + 3x 2 x 3 + x 2 8 x 12. X2( - ii. %%give%the%denominator%in%factored%form. % iii. %%give% r( x) %in%factored%form. % If%the%answer%to%any%question%is% none, %state% none. %%answers%left%blank%will%be%marked%incorrect. % (a)% i. %%give%the%numerator%in%factored%form. % (b)%%find%any%and%all%asymptotes%of% r( x) . % (c)%%find%any%and%all%intercepts%and%holes%of% r( x) . %%give%your%intercepts%and%holes%in%terms%of%their%(x,%y)%coordinates. % (d)%%sketch%the%graph%of% r( x) . %%your%sketch%should%clearly%show%the%asymptotes%and%intercepts. % (e)%%what%is%the%domain%of% r( x) ?% n ,=. xityx ?3. ,"sdenominator by intercepts @ c- 3,0 : a .
