please solve the questions in the two files, thank you. no need to show all the work.Mohammed Yaaseen Gomdah
MATH
203
Winter
2016 F
WeBWorK assignment number Assignment
9
W14 is due : 03/23/2016 at 03:00am EDT.
The
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for the course contains the syllabus, grading policy and other information.
This ?le is /conf/snippets/setHeader.pg you can use it as a model for creating ?les which introduce each problem set.
The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making
some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are
having trouble ?guring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor for
help. Don’t spend a lot of time guessing – it’s not very ef?cient or effective.
Give 4 or 5 signi?cant digits for (?oating point) numerical answers. For most problems when entering numerical answers,
you can if you wish enter elementary expressions such as 2
?
3 instead of 8,
sin
(
3
*
pi
/
2
)
instead of 1,
e
?
(
ln
(
2
))
instead of 2,
(
2
+
tan
(
3
))
*
(
4

sin
(
5
))
?
6

7
/
8 instead of 27620.3413, etc. Here’s the
list of the functions
which WeBWorK understands.
You can use the Feedback button on each problem page to send email to the professors.
1.
(1 pt) Use linear approximation to estimate the amount
of paint in cubic centimeters needed to apply a coat of paint
0
.
020000 cm thick to a hemispherical dome with a diameter of
50
.
000 meters.
2.
(1 pt) Let
y
=
5
x
2
+
7
x
+
2.
Find the differential
dy
when
x
=
1 and
dx
=
0
.
2
Find the differential
dy
when
x
=
1 and
dx
=
0
.
4
3.
(1 pt) Let
y
=
tan
(
4
x
+
3
)
.
Find the differential
dy
when
x
=
2 and
dx
=
0
.
4
Find the differential
dy
when
x
=
2 and
dx
=
0
.
8
4.
(1 pt) Let
y
=
2
x
2
.
Find the change in
y
,
?
y
when
x
=
4 and
?
x
=
0
.
3
Find the differential
dy
when
x
=
4 and
dx
=
0
.
3
5.
(1 pt) Let
y
=
3
?
x
.
Find the change in
y
,
?
y
when
x
=
1 and
?
x
=
0
.
1
Find the differential
dy
when
x
=
1 and
dx
=
0
.
1
6.
(1 pt) The linear approximation at
x
=
0 to
?
2
+
5
x
is
A
+
Bx
where
A
is:
and where
B
is:
7.
(1 pt) The linear approximation at
x
=
0 to
1
?
2

x
is
A
+
Bx
where
A
is:
and where
B
is:
8.
(1 pt) Let
f
(
x
) =
6
x
3
+
3. Find the open intervals on which
f
is increasing (decreasing). Then determine the
x
coordinates
of all relative maxima (minima).
1.
f
is increasing on the intervals
2.
f
is decreasing on the intervals
3.
The relative maxima of
f
occur at
x
=
4.
The relative minima of
f
occur at
x
=
Notes:
In the ?rst two, your answer should either be a single
interval, such as (0,1), a comma separated list of intervals, such
as (inf, 2), (3,4), or the word “none”.
In the last two, your answer should be a comma separated list
of
x
values or the word “none”.
9.
(1 pt) Let
f
(
x
) =
x

2
x
+
2
. Find the open intervals on which
f
is increasing (decreasing). Then determine the
x
coordinates
of all relative maxima (minima).
1.
f
is increasing on the intervals
2.
f
is decreasing on the intervals
3.
The relative maxima of
f
occur at
x
=
4.
The relative minima of
f
occur at
x
=
Notes:
In the ?rst two, your answer should either be a single
interval, such as (0,1), a comma separated list of intervals, such
as (inf, 2), (3,4), or the word “none”.
In the last two, your answer should be a comma separated list
of
x
values or the word “none”.
10.
(1 pt) Let
f
(
x
) =
4

4
x
+
4
x
2
. Find the open intervals
on which
f
is increasing (decreasing). Then determine the
x

coordinates of all relative maxima (minima).
1.
f
is increasing on the intervals
2.
f
is decreasing on the intervals
3.
The relative maxima of
f
occur at
x
=
4.
The relative minima of
f
occur at
x
=
Notes:
In the ?rst two, your answer should either be a single
interval, such as (0,1), a comma separated list of intervals, such
as (inf, 2), (3,4), or the word “none”.
In the last two, your answer should be a comma separated list
of
x
values or the word “none”.
Generated by the WeBWorK system c
±
WeBWorK Team, Department of Mathematics, University of Rochester
1
Answer