limxc f (x) = L if and only if limxc f (x) = L and
limxc+ f (x) = L
-Given a function f , we say that f is continuous at x = c if we can
draw the graph of f without lifting our pencil at x = c. (This is
not a precise definition.)
-Definition
A function f
Theorem (The Sandwich Theorem)
If f (x) g(x) h(x) for all x in an open interval that contains c
(except possibly at c) and
Lim xc
f (x) = lim xc
h(x) = L
then
lim xc
g(x) = L.
-We can use the Sandwich Theorem to find a couple of limits that
we will need l
FINAL EXAM-MATH 1300
FALL TERM, 2012
R. Blute, T. Kousha, C. Starling & C. Zhong
Please circle the name of your professor above.
First Name:
Last Name:
I.D. Number
Instructions-This nal examination consists of 10 multiple choice questions worth 4 points
e
Multiple Choice Section Questions (15)
Question 1 On what interval is the following function concave down?
f(x)=w4+2x312:c2+w+5
A) (0,4) B) (-2,1) C) (1,4) D) (3,2) E) (-1,3)
le)° LL? eff a H
"h kkm JAM pm 3_ b _ O +
.1 \9( X16} 4) v 0 U
- U (Ml) (3w)
Que
FINAL EXAM-MATH 1300
FALL TERM, 2006
R. Blute & P. Boily
Name(Print LEGIBLY)
I.D. Number
Instructions-This nal examination consists of 10 multiple choice questions worth 3 points
each. Your answers to the multiple choice questions must be clearly marked i
-Theorem (Reflecting a Graph)
To obtain the graph of:
f (x) reflect the graph of f (x) about the horizontal axis
f (x) reflect the graph of f (x) about the vertical axis
-The logarithmic scale
good for applications where values differ by many orders of
ma