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Math 1431: 2.3, 2.4 Lecture problems for class
Warm-up from 2.1,2.2
The Use of Time in Applications in 2.3
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2.3 Business Applications:
Supply & Demand……..Market Equilibrium
ost !unction
"e#enue $unction
%rot $unction
1. !ost " #ariable !osts $ %i&e' !osts
2. (eenue " )umber of items sol' times the *rice of each
3. *ro+t" (eenue !ost
Three more mportant usiness functions
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Supply !unctions' p ( S)*+
Demand $unctions' p ( D)*+
Equilibrium %oints: S)*+ ( D)*+
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/b0 etermine the uantit 'eman'e' hen the unit price is set at
p " 54. /6ie
our anser correct to the nearest full unit.0
3000 units
etermine the price at hich the supplier ill ma7e
1,288 units of the commo'it
aailable in the mar7et. /6ie our anser correct to the nearest
cent.0
517.93
)9T: 1;.
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$i,ure - ote /c: -02/1
2. 4e 5imit: Denition
E#aluation o! 5imits
Al>ebra an' 'irect substitution
aluation from a >raph of a function
aluation of limits as & approaches $?- in+nit
@(eal Worl' Application
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4e !unction ! 4as t4e limit 5 as * approac4es a' 6ritten
lim* 7 a !)*+ ( 5
i! t4e #alue o! !)*+ can be made as close to t4e number 5 as
6e
please by takin, * su8ciently close to )but not equal to+ a.
lim ) 9 *2+* 7 -
lim ;) * < /3+
* 7 = 2
lim /9 * 7 = 2
5imits !rom ,rap4s
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Lim & 1"
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
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>E?"EM : $or all n@1' lim -*n ( 1
*7
and lim -*n ( 1
*7 =
pro#ided t4at -*n is dened.
Cn e#aluatin, limits at hest poer of & is in the numerator,
the limit as *7 < or =
does not e*ist.
f the hi>hest poer of & is in the 'enominator, the limit
as *7 < or
equals 1.
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f the hi>hest poer of & in the numerator is the same as
the hi>hest poer
of & in the 'enominator, the limit as *7 < or = is t4e
ratio o! t4e
coe8cients o! t4ose t6o terms.
Fo back to problem - and no6 6ork.
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