This preview shows pages 1–3. Sign up to view the full content.
Math 1110
Prelim I (9/27/2011)
1
Question 1.
(10 points) The National Oceanic and Atmospheric Administration collects climate
data at weather stations around the US. The chart below shows the total rainfall to date (beginning
June 1, 2006) observed at the Binghamton, NY, station during the month of June 2006. The dots
indicate the measurement at the end of the corresponding day.
30#,4.5/6#' 78
9 0#:4
& 0#:4$;
= 0#:4$;
9( 0#:4$;
>05$
+56"#/
61 .0#1.22
(a) What was the total rainfall in Binghamton in June, 2006?
The total rainfall in June, 2006, was approximately
11.3
inches. We accepted any answer that
was strictly greater than 11 or less than 11.6 for full credit.
(b) Estimate the average rate of rainfall from June 1 through 4, 2006.
The average rate of rainfall was approximately
f
(
4
) 
f
(
0
)
4

0
=
2.2
4
=
0.55
inches per day
.
We also accepted
f
(
4
)
f
(
1
)
4

1
, and slightly different approximate values for
f
(
4
)
.
(c) On which day was the rain falling the most heavily? How can you tell?
It was falling the most heavily on June 27, 2011, because the slope of the graph is the steepest
on that day.
(d) The graph of these data exhibits increasing behavior. Would we ever see a decrease for this
function? Why or why not?
You will never see a decrease because these are cumulative data: each days rainfall is added
to the previous total. Since it can never “unrain,” the function either increases or remains
constant. (The data do not include evaporation either!)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentMath 1110
Prelim I (9/27/2011)
2
Question 2.
(28 points) Evaluate the following expressions, or explain why you cannot. You may
(a)
D
omain
±
ln
(
x
)
x

1
²
= (
0,1
)
∪
(
1,
∞
)
or all positive real numbers not equal to
1
.
(b) cos
(
log
9
(
3
π
)
)
=
cos
(
π
log
9
(
3
)
)
=
cos
³
π
·
1
2
´
=
cos
±
π
2
²
=
0.
(c) Find a value of
x
so that arcsin
(
sin
(
x
))
6
=
x
. The value
x
=
π
satisﬁes this, because
arcsin
(
sin
(
π
)) =
arcsin
(
0
) =
0
6
=
π.
(d) lim
x
→

1
x
2

1

x


1
If
x < 0
then

x

= 
x
and so
lim
x
→

1
x
2

1

x


1
=
lim
x
→

1
x
2

1

x

1
=
lim
x
→

1
(
x

1
)(
x
+
1
)
(
x
+
1
)
=
lim
x
→

1
(
x

1
) =
2.
This is the end of the preview. Sign up
to
access the rest of the document.
 '06
 MARTIN,C.

Click to edit the document details