Part II: The Answers
278
Answers
401–500
423.
1
3
Use the formula for the differential, dy = f
'(x)
dx:
y x
x
dy
x
dx
=
−
= ( − )
2
4
2
4
So for the given values, x = 3 and dx = 1
6
, find dy:
dy = (
− )
= ( ) =
2 3 4 1
6
2 1
6
1
3
( )
424.
1
20
Use the formula for the differential, dy = f
'(x)
dx:
y x
dy
x
x dx
dy
x
x
dx
=
+
= (−
+
)
= −
+
−
1
1
1
1
2
2
1
2
2
2
2
2
(
) ( )
(
)
So for the given values, x = 1 and dx = –0.1, find dy:
dy =
−
+
−
= − −
=
2 1
1 1
0 1
1
2
1
10
1
20
2
2
( )
( )
( )
( )
.
425.
− 3
100
Use the formula for the differential, dy = f
'(x)
dx:
y
x
dy
x
x dx
dy
x
xdx
=
=
−
= −
cos
(cos )( sin )
cos sin
2
2
2
So for the given values, x = π
3
and dx = 0.02, find dy:
dy = −
= −
=
−
2
3
3
0 02
2 1
2
3
2
2
100
3
100
cos sin ( . )
π
π
(
)
( )
( )
278
Answers
401–500
423.
1
3
Use the formula for the differential, dy = f
'(x)
dx:
y x
x
dy
x
dx
=
−
= ( − )
2
4
2
4
So for the given values, x = 3 and dx = 1
6
, find dy:
dy = (
− )
= ( ) =
2 3 4 1
6
2 1
6
1
3
( )
424.
1
20
Use the formula for the differential, dy = f
'(x)
dx:
y x
dy
x
x dx
dy
x
x
dx
=
+
= (−
+
)
= −
+
−
1
1
1
1
2
2
1
2
2
2
2
2
(
) ( )
(
)
So for the given values, x = 1 and dx = –0.1, find dy:
dy =
−
+
−
= − −
=
2 1
1 1
0 1
1
2
1
10
1
20
2
2
( )
( )
( )
( )
.
425.
− 3
100
Use the formula for the differential, dy = f
'(x)
dx:
y
x
dy
x
x dx
dy
x
xdx
=
=
−
= −
cos
(cos )( sin )
cos sin
2
2
2
So for the given values, x = π
3
and dx = 0.02, find dy:
dy = −
= −
=
−
2
3
3
0 02
2 1
2
3
2
2
100
3
100
cos sin ( . )
π
π
(
)
( )
( )