9.
(12 pts.)
Evaluate each of the following limits.
If a limit fails to
exist, say how as specifically as possible.
(a)
lim
x
→ π
sin(
x
)
x
π
(b)
lim
x
→
∞
1
3
x
x
(c)
lim
x
→
0
x
tan(
x
)
x
3
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentTEST3/MAC2311
Page 5 of 5
______________________________________________________________________
10.
(20 pts.)
When f is defined by
and
.
(a)
(3 pts.)
What are the critical point(s) of f and what is the value of f at each critical point?
(b)
(3 pts.)
Determine the open intervals where f is increasing or decreasing.
(c)
(3 pts.)
Determine the open intervals where f is concave up or concave down.
(d)
(3 pts.)
List any inflection points or state that there is none.
(e)
(3 pts.)
Locate any xintercepts of
f
, or state that there isn’t any.
(f)
(5 pts.)
Carefully sketch the graph of f below by plotting a few essential points and then connecting the dots
appropriately.
y
x
______________________________________________________________________
Silly 10 point Bonus Problem:
Show
ln(
x
1)
≤
x if x
≥
0.
[Say where your work is, for it won’t fit here!]
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 STAFF
 Calculus, Derivative, Differential Calculus, Convex function, Stationary point

Click to edit the document details