Part II: The Answers
490
Answers
801–900
Notice that if you substitute in the value x = 2, you get the indeterminate form 0
0
.
Use L’Hôpital’s rule to find the limit:
lim
lim
x
x
x
x
x
x
→
→
−
+ −
=
+
=
( )+
=
2
2
2
2
6
1
2 1
1
2 2 1
1
5
803.
∞
The given problem is
lim cos
sin
x
x
x
→ ( )
−
−
π
2
1
Notice that if you substitute in the value x = π
2
, you get the indeterminate form 0
0
.
Using L’Hôpital’s rule gives you the limit:
lim cos
sin
lim
sin
cos
lim tan
x
x
x
x
x
x
x
x
→ ( )
→ ( )
→ ( )
−
−
−
−
=
−
−
=
= ∞
π
π
π
2
2
2
1
804.
0
Start with the given problem:
lim cos
tan
x
x
x
→
−
0
1
Notice that if you substitute in the value x = 0, you get the indeterminate form 0
0
. Use
L’Hôpital’s rule to find the limit:
lim cos
tan
lim sin
sec
sin
sec
x
x
x
x
x
x
→
→
−
=
=
= =
0
0
2
2
0
1
0
0
1
0
805.
0
Here’s the given problem:
lim ln
x
x
x
→∞
2
Notice that if you take the limit, you get the indeterminate form ∞
∞
. Using L’Hôpital’s
rule gives you the limit as follows:
lim
lim
x
x
x
x
x
→∞
→∞
=
=
1
2
1
2
0
2
806.
− 2
π
Here’s the given problem:
lim
ln
cos
x
x
x
→
( )
1
2
π