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Tutorial
Class
Instructor:
John
O'Reilly
Max/Min
Word
Problems:
1.
A
farmer
has
1000
metres
of
wooden
fencing,
and
she
wishes
to
fence
off
a
rectangular
plot
of
land
bordered
by
a
river,
so
that
she
does
not
require
fencing
on
the
side
of
the
rectangle
adjacent
to
the
water.
Find
the
dimensions
of
the
rectangular
plot
with
the
greatest
possible
area.
ANS:
Dimensions
500
m
by
250
m
2,
A
rectangular
field
is
to
be
fenced
on
all
four
sides
and
then
divided
into
two
fields
with
a
fence
parallel
to
two
opposite
sides.
If
the
total
fencing
available
is
200m,
what
dimensions
will
give
the
maximum
enclosed
area?
ANS:
Dimensions
lgo
m
by
50m
3.
A
closed
box
with
a
square
base
is
to
have
a
volume
of
10
m®.
The
base
cost
$4/m?,
the
sides
cost
$2/m?
and
the
top
cost
$1/m*.
What
dimensions
will
give
the
minimum
cost
to
build
the
box?
ANS:
Dimensions
2mx
2mx
5/2
m
4.
A
manufacturer
wishes
to
design
an
open
box
having
a
square
base
and
a
surface
area
of
108
square
metres.
What
dimensions
will
a
box
be
of
maximum
volume?
ANS:
6mx
6m
x
3m
Evaluate
each
of
the
following
limits
(L'Hopital's
Rule):
In(sec
2x)
]
1
1
i
VRS
ANS:
2
6.
mum({L17)
ans:
1
p
AN
.
xX1
.
2.
lm(%
ANS:
1
7.
mi
ANS:
0
5.
g
A0x)
ANS:
0
8.
liml=C0S'X
ang:
3
xw
X2
=
0
sin'*x
=
2
4.
lim(12x0"
Ans:
L
9.
1im&3%
ANS:
In3
"
€
x~0
e3>
_
e
3%
)
1x+Inx
.
1