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MATH 1080 (11)
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Department
Mathematics
Course
MATH 1080
Professor
Joe Cunsolo
Semester
Fall

Description
Lab Section !1 SOLUTIONS WHITE 01 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 $.97 cm. Use differentials to determine the approximate change in the surface areaßWœ%of the balloon. SOLUTION Surface area of the sphere W œ %1< ß < ! %ß .< œ  !Þ!$ . ÞÞÞÞÞÞ " Approximate change in the surface area .W œ )1Ñ œ "#> 2 litres/hour. Determine the equation of ZÐ>Ñ , the amount of water (in litres) lose hours, if the amount of water lost a>œtim 2 hours wasl%es. 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 = %>  #>  * 3. Find the third order Taylor Polynomial approximation of 0ÐBÑœ#/$B' abButœ# . ! SOLUTION w 0Bw()0 0 2 B3)www " 0ÐBÑ ¸ 0 B ( 0 0 0 0 ) (B  B )0+ 2! B  0 ) + 3! (B  B ) .ÞÞÞÞÞÞ# For 0( ) / $B' and B = 2: 0 3 0ÐBÑ œ#/ $B' 0 œ()/ $œ#/ œ# ! $B' $Ð#Ñ' 0 (B) œ '/ 0 (#) œ '/ œ '/ œ ' ww $B' ww $Ð#Ñ' ! "
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