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# Quiz3V2

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University of Guelph

Mathematics

MATH 1080

Joe Cunsolo

Fall

Description

Lab Section !1 SOLUTIONS YELLOW 01 MATH 1080 Lab Quiz #3 Y
No Calculators Allowed
Surname: Initials:_________ Lab Section #:________
(PRINT)
Student #: Class Section #:_______
1. The gas in a spherical balloon contracts causing a reduction in the radius of the ballo#n from &cm. to
%.9 cm. Use differentials to determine the approximate change in the surfaßeaÑ œ *> & litres/hour. Determine the equation of
ZÐ>Ñ , the amount of water (in litres) loste hours, if the amount of water lost at>œim 2 hours
wasl%res.
SOLUTION
2 $
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>Ñ = $> &> ""
#B)
3. Find the third order Taylor Polynomial approximation of 0ÐBÑœ#/ abButœ% ! ..
SOLUTION
ww www
0ÐBÑ ¸ 0 B ( ) + 0 B ) (B B ) + 0B ()0 (B B ) + 3) (B B ) . ÞÞÞÞÞÞ"
0 0 0 0 2! 0 3! #
#B)
For 0B( ) / and B % =0:
3
#B) #%() ) !
0ÐBÑ œ#/ 0 % œ( / œ#/ œ#

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