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Unformatted text preview: 34B Midterm II Winter 2006
March 3, 06 Instructor: Prof Wei (WA/ﬁe Print your Name
Circle your TA’s name and Discussion time:
Melissa Banister Benjamin Benoy Thomas Howard
M 4pm; 5pm; 6pm; 7pm; T 8am ; 5pm; 6pm; 7pm rlbtal Score: 50
Your Scores: 1‘ 2 3, ....... H 4, .... ,r 5" ....... M Your Total Books, notes are NOT allowed READ the problems carefully~ No calculators are allowed Put
ﬁnal answers on boxes on this page Put high quality work in the blue book for all answers. Points
might be awarded for this: Number your solutions in the blue book; At the end of exam STAPLE
this page to the INSIDE front blue cover of the blue book, so that this side faces the white writing
pages of the blue book. 1. (10 pts) (a) a What is the enerai solution of y” t = Esiiit—Z?
g 3 .. ..
5%:“25/llt“f +f—{1L +C1 (c) What is the general solution of y’(t) = 4—211? 2‘ (10 pts) Find the local max and min of Mari + 12$ + 4‘. Clearly show how you applyr the
second derivative test. . . . x: . . 3::
local minimum IS .. I 1 when W Z local maxnnum lS 0 when 2 3. (10 pts) A tank initially contains 1000 liters of pure water. rThen water containing 4 mg of
detergent per liter starts to enter the tank at the rate of 20 liter per hour, How long until the average
concentration of detergent in the tank is 2 mg per liter? How long until the average concentration . I l’"
of detergent in the tank is x mg per liter? 5 0 X , ‘/_ 4. (10 pts) Find the linear approximation of f(m) = a: + 463$ at :1: = 0. X~) a z {I 6 J; X
5‘ (10 pts) A lava is cooling down according to Newton’s iaw of cooling, The initial temperature
of the lava is 500°C. The temperature of the surrounding is 30°C. rThe initial rate at which the lava
cools is 70° C per day. (a) What is the differential equation which describes the temperature of
lava? (b) What will the temperature of lava be after 5 days? 3433 Midterm II Winter 2906
March 3, 06 instructor: Prof) Wei
8 [Li e Print your Name Circie your TA’s name and Discussion time:
Melissa Banister Benjamin Benoy rThomas Howard M 4pm; 5pm; 6pm; 7pm; T 8am; 5pm; 6pm; 7pm Total Score: 50 _
Your Scores: 1. 2 ......... H 3. ....... M 4. 5. Your Total Books, notes are NOT aliowed. READ the problems carefully. No caiculators are allowed. Put
ﬁnai answers on boxes on this page. Put high quality wort: in the blue book for all answers, Points
might be awarded for this: Number your soiutions in the blue book; At the end of exam STAPLE
this page to the INSIDE front blue cover of the blue book, so that this side faces the white writing pages of the biue book 1. (10 pts) (a) ,1
jzvszxf Mir + c),
(b) 1
yirﬂadr’wf +Sf’ +3 (a) What is the generai solution of y” = 2 cos t—Z? (b) What is the particular solution of (a) for which if (0) = 3, y(0) m 1? (c) What is the generai soiution of y’ = 6—2y? 2 (10 pts) Find the iocal max and min of «~4st + 6:1: + 12. Cleariy show how you apply the
second derivative test. .  . x: . . X:
local minimum is X/ when // local maxrrnum IS / é when / 3‘ (10 pts) A tank initially contains 500 liters of pure water. Then water containing 4 mg of
detergent per liter starts to enter the tank at the rate of 20 iiter per hour, How long until the average
concentration of detergent in the tank is 2 mg per liter? How long until the average concentration of detergent in the tank is 1: mg per liter? Afarmﬁ
\/__ til (10 pts) Find the linear approximation of f = :1: + 9633 at m = 0. (r) (E; 3 “f X 5. (10 pts) A lava is cooiing down according to Newton’s law of cooling The initial temperature
of the lava is 1000°C. The temperature of the surrounding is 40°C. The initial rate at which the
lava cools is 100° C per day. (a) What is the differential equation which describes the temperature of lava? (b) What will the temperature of lava be after 5 days? ...
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This note was uploaded on 12/27/2011 for the course MATH 5B taught by Professor Rickrugangye during the Fall '07 term at UCSB.
 Fall '07
 RickRugangYe

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