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Unformatted text preview: Calculus II Midterm 2 March, 2009 2 l. (3 marks each: total 9 marks) Answer each question in the space provided. You
MUST show your work. a) A tank contains 100 L of brine, with a concentration of 0.3 kg of salt per liter.
Pure water enters the tank at a rate ofS Limin, The solution is kept thoroughly
mixed and drains From the tank at the same rate. What is the amount of salt in the tank. Ala), as a function of time I? b) Use Euler‘s Method to approximate y(1.2) with step size h = 0.1 for the following initial value problem:
y'= x—y, y(1) = 0 _ )_ . dy _7r/
c) If x— 005: and } — 251n(3t),ﬁnd Ewhen (— /6. Calculus II Midterm 2 March, 2009 2. (5 marks) Suppose the average time waiting in line to purchase movie tickets at some
Cineplex is 8 minutes. What is the probability ofwaiting more than 10 minutes? Calculus II Midterm 2 March, 2009 4 3. (9 marks) Suppose that a corpse was discovered in a motel room at midnight and its
temperature was 80°F. The temperature of the room is kept constant at 60°F . Two
hours later the temperature of the corpse dropped to 75° F , Find the time of death, Note:
The temperature of a corpse at time of death is 98.6”17 dT
Hint: Newton’s Law ofCooling is given by d: : k(T _ ) where TN is the temperature of the surroundings. Calculus II Midterm 2 March, 2009 4. (9 marks) Find the area of one loop of the polar curve 7” 2 2 C0368) . Calculus II Midterm 2 March, 2009 5. (2 marks each: total 8 marks) Indicate whether each of the following statements is
true (T) or false (F) and J USTIFY your answer. You will receive credit only if your
answer is correct AND properly justiﬁed. a) All solutions of the differential equation y’ = y2 + 5 are increasing ﬁmctions. Answer: Justiﬁcation: b) y : sin x + cosx is a solution ofthe differential equation y ’ — y = 0. Answer: Justiﬁcation: c) The parametric curve shown below represents the parametric equations
x=cos!, yztz. Answer: Justiﬁcation: d) The two parametric Curves y : 35in! and x : cost can be converted to the 2 Cartesian equation x3 + y— :1? 9
Answer: Justiﬁcation: Calculus II Midterm 2 March, 2009 'r' 6. (Total 10 marks) Answer each of the following in the space provided. You do NOT
have to show your work for this question, but you may do so if you wish (eg. for part
marks in case the ﬁnal answer is wrong). a) (2 rk _ 3C) 8 Xi th orce ece ar toXﬁ/X/W
e on i n ura en he 0. etﬂdaﬁ M: ed t str chﬂle/
' 0 2 t , . .
n e icahm we dldh‘l' COW HMS b) (2 a ) S tu ani gr lthat :lylates VWsry/dwned’by
r a'ngth cu ey—V’;,wh eO x5),/:1 ut x 15.
Icahn). ‘l'lms wag; Mid‘rwm ll“— l
mamaﬂ
c) (2 marks) Find the length ofthe curve x = (3082191 y = sin 26’ , 0 S :9 S 72'. d) (2 marks) Consider the direction ﬁeld shown below. fr'u—‘u—‘w—‘d—d—rd —L—~—L—n‘——H‘uHHH frﬂ/fr’www—a— F
l
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l
‘u
t
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t
x uh
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f
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f Which of the following differential equations does it correspond to? Circle the
correct answer. . , 7. .. , x2 —l 1) y —— 11) y = y .V iii) y’ =szinx iv) y’=x’—y3 e) (2 marks) Find a Cartesian equation for the curve represented by I" = 2 ...
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 Spring '11
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