Andrew Robert Border

Homework 2
due
Fri, Oct 9
at 11:59 pm
Course: math151au09es
This problem set covers Sections 2.5  2.9.
Recitation Call#: .
Carefully read all instructions for entering answers into WeBWorK.
Set: Hmwk2
1.
(2 pts)
[rgb]0,0.07,0.45 Click on the graph to get an enlarged view.
Let the function
f
(
x
)
be given by the depicted graph on the
interval
[

6
,
10
]
.
List, in order, the maximal intervals on which
f
is continu
ous, separated by commas.
[rgb]0,0.07,0.45 Include endpoints at which
f
(
x
)
is onesided continuous on the
respective interval by square brackets [rgb]0.6,0,0 ’[’ or [rgb]0.6,0,0 ’]’ ,
and exclude endpoints by [rgb]0.6,0,0 ’(’ or [rgb]0.6,0,0 ’)’ where
f
(
x
)
is dis
continuous.
Indicate the values of
x
where
f
(
x
)
is discontinuous. Start
with the leftmost point. For each of the values state whether
f
(
x
)
is continuous from the right (input R), or from the left (in
put L).
at
x
=
f
(
x
)
is continuous from
;
at
x
=
f
(
x
)
is continuous from
;
at
x
=
f
(
x
)
is continuous from
.
2.
(2 pts) Use continuity to evaluate
lim
x
→
1
e
x
4

x
2
Enter
I
for
∞
,
I
for

∞
, and
DNE
if the limit does not exist.
Limit =
3.
(2 pts)
Let
f
(
x
) =
±
mx

10
,
if
x
<

7
x
2
+
9
x

3
,
if
x
≥ 
7
If
f
(
x
)
is a function which is continuous everywhere, then we
must have
m
=
Now for fun, try to graph
f
(
x
)
.
4.
(2 pts) For what value of
c
is the function deﬁned below
continuous on
(

∞
,
∞
)
?
f
(
x
) =
±
x
2

c
2
,
x
<
8
,
cx
+
80
,
x
≥
8
.
c
=
5.
(1 pt) Use the Intermediate Value Theorem to check
whether the equation
x
3

3
x

6
.
9
=
0 has a root in the interval
(
0
,
1
)
.
Check
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 Fall '08
 Any
 Math, Derivative, lim, pts, Continuous function

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