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MATH 1080 (10)
Quiz

# Quiz3V3

2 Pages
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School
University of Guelph
Department
Mathematics
Course
MATH 1080
Professor
Joe Cunsolo
Semester
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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