NATIONAL
UNIVERSITY
OF
SINGAPORE
Department of Mathematics
MA
1505 Mathematics I
Tutorial 7
1.
Imagine you are visiting a country in the winter season. Let
T
(
x, y
) = 36

1
5
[
x
2
+ (
y

5)
2
]
be the temperature at location (
x, y
) in a 10ft
×
10ft hotel room with a heater on at night.
One corner of the room is at (0
,
0) and the opposite corner is at (10
,
10).
(i)
What is the domain of the temperature function?
(ii)
Where is the likely location of the heater?
(iii)
Suppose you like to sleep within the temperature range of 20
◦
C to 25
◦
C. Where would
you put your bed?
(iv)
Determine the locations in the room where the temperature is lowest.
Ans
. (ii)
(0
,
5);
(iv)
(10
,
0) and (10
,
10).
2.
In an electric circuit, the voltage of
V
volts (V), current of
I
amperes (A), and resistance of
R
ohms (Ω) are governed by Ohm’s Law
V
=
I
×
R.
(i)
If the resistance is fixed at 15 Ω, how fast is the current increasing with respect to
voltage?
(ii)
If the voltage is fixed at 120 V, how fast is the current increasing with respect to resistance
at the instant when resistance is 20 Ω?
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 Spring '11
 phoon
 local maximum, 4j, Department of Mathematics, 10ft

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