300672A09TutorialForWeek12.doc
300672 Mathematics 1A
Autumn 2009
Tutorial for Week 12
The starred
*
questions will be discussed in tutorials. Solutions for the others will be posted on vUWS.
Question 1
(a)
A metal circular disc contracts during cooling. If its radius decreases at the rate of
0.003 cm/s, how fast is the area of its face decreasing when its radius is 10cm?
(b)
A water tank has the shape of an inverted circular cone with base radius 4m
and height 7m. If water is pumped into the tank at a rate of 2m
3
/min, find the
rate at which the water level is rising when the water is 5m deep.
(c)
*
A runner sprints around a circular track of radius 100m at a constant speed of
7m/s. The runner’s friend is standing at a distance of 200m from the centre of
the track. How fast is the distance between the runner and her friend changing
when the distance between them is 200m?
Question 2
(a)
Use the formula
)
(
'
)
(
)
(
)
(
a
f
a
x
a
f
x
f

+
≈
to approximate
1
4
.
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 Spring '09
 ChalesZworestine
 Math, Derivative, Differential Calculus, Convex function, dx dx dx, dU dx dx

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