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# Quiz3V3

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University of Guelph

Mathematics

MATH 1080

Joe Cunsolo

Fall

Description

Lab Section !2 SOLUTIONS WHITE 02 MATH 1080 Lab Quiz #3 W
No Calculators Allowed
(PRINT)e: Initials:_________ Lab Section #:________
Student #: Class Section #:_______
1. The gas in a spherical balloon contracts causing a reduction in the radius of the balloon from $cm. to
#Þ*) cm. Use differentials to determine the approximate change in the volumeß Z$œ 1< ß of the
balloon.
SOLUTION
Volume of sphere Z œ % 1< ß < œ $ß .< œ !Þ!# . ÞÞÞÞÞÞ "
$ !
Approximate change in the volume .Z œ %1< .Ñ œ *> #> litres/hour. Determine the equation of
ZÐ>Ñ , the amount of water (in litres) loste hours, if the amount of water lost a>œtim 2 hours
wasl$es.
SOLUTION
VÐ>Ñ = ' VÐ>Ñ.> = (*> + #>) .> œ $> > G ÞÞÞÞÞÞ "
When > œ #ß Z Ð#Ñ œ $# œ $Ð#Ñ Ð#Ñ G
Ê $#œ#%%G Ê G œ%
Answer ÞÞÞÞÞÞ"
2
VÐ >=>%$ #
#B'
3. Find the third order Taylor Polynomial approximation of 0ÐBÑœ$/ abButœ$ ! .
ww www
0ÐBÑ ¸ 0 B ( 0 0 00B ) (B B )0+ 0B() 0 (B 0B ) +3) (B B ) .ÞÞÞÞÞÞ"
2! 3! #
#B'
For 0B( ) / and B $ 0 :
3
#B' #Ð$Ñ' !
0ÐBÑ œ$/ 0 $ œ($) œ$/ œ$
0 (B) œ '/ #B' 0 ($) œ '/ #Ð$Ñ' œ '/ œ '
#B'
0 (B) œ "#/ 0 ($) = "#/ #Ð$Ñ' œ "#/ œ "# ÞÞÞÞÞÞ "
#B' #
0 (B) œ #% / 0 ($) œ #% / #Ð$Ñ' œ #%

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