MATH
1441
Test Number 1
SPntornh",.
1
Ii
')nn~
NAME:
~_"""'__==___~~-::....-
__
PLEASE
BE
NEAT, AND
EXCEPT
FOR
THE
TRUE-FALSE QUESTIONS,
SHOW
YOUR
WORK.
1.
Circle T if
and
only if
the
statement
is
true.
(2
points each)
T
1.
If
f : (0,1)
-4
~
is continuous
at
x =
!'
then
f is differentable
at
x =!.
T
2.
If
lim(j·
g)(x) exists, then
limf(x)
and
limg(x) each exist.
x-+a
x-+a
x--+a
x3
+1
0~x<2
\
T 3.
If
f(x)
= 9,' x =
2,
, then f is continuous
at
x =
2.
(
{ x +7,
2<x<3
T
4.
If
lim
~(x)
= 7
and
lim
f(x)
=
0,
then
lim g(x) =
O.
x--+a
9X
x--+a x--+a
T
5.
Let g :
[a,
b]
-----+ R
If
cE
(a,
b)
and
lim g(x) =
4,
then
there exists
x~c
an
interval I containing c such
that
g(x) > 3.5 for each x in
I, .except possibly for x =
c.
II.
In
each of
the
following, find
the
limit if
it
exists.
If
it
does
not
exist, so
indicate.(6 points each)
a. lim x 2
-x-2
b.
lim
sin
4x
c.
lim
y'9±h-3
x~2
:1:-2
x~O
x cos
4x
h~O
h
ADDITIONAL
PROBLEMS
ON
THE
BACK
1
