Evaluate the following limits.
If
they don't exit,
write NO.
a) lim 50Ox2
-2x
+5
b) tim
500x1-Zx
+5
x-+co 25Ox
+1000
x+0
25Ox
+1000
c)
lim 3x'-2x-7
x-+-1 5xo
+7x2
-1
e)
lim
*'-
81
x-+9 x-9
d) lim
*'
-
27
x-+-3
x
+
3
State whether or not
the following
functions
are continuous
at the indicated point
If
not,
give
reason(s)
why.
a) f(x)
:
*'
-
81
atx: 9
x-9
b) f(x)
=
xz
+
36
at x:
-6
x+6
f
2*
+to,
if
D2
c)
(x);
,{
atx:2
/
g+l*
if
x<2
\,
d)
f(x)
=
5x'+ 17
at x=
-l
x- 1
Given
f
'(x) =
5
+
7x.
Find the
x values for
which
f decreases.
Use the definition
of the
derivative
to
compute f
'(x)
for
f(x)
=
-5 -]lx -2x2
f) lim
3-\tffi
x+ -3
x*3
Find
the
average rate
of change
of
f(x)
=
*'+
5x - 8
between
x
=0.8
and x=1.