103
Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions, and L’Hôpital’s Rule
Evaluating Indeterminate
Forms Using L’Hôpital’s Rule
800–831 If the limit is an indeterminate form,
evaluate the limit using L’Hôpital’s rule. Otherwise,
find the limit using any other method.
800. lim
x
x
x
→−
+
+
1
3
1
1
801. lim x
x
x
→
−
−
1
4
3
1
1
802. lim x
x
x
x
→
−
+ −
2
2
2
6
803.
lim cos
sin
x
x
x
→ ( )
−
−
π
2
1
804. lim cos
tan
x
x
x
→
−
0
1
805. lim ln
x
x
x
→∞
2
806.
lim
ln
cos
x
x
x
→
( )
1
2
π
792. coth x dx
∫
793. sech
2 3
2
x
dx
−
(
)
∫
794.
sech
tanh
2
2
x
x
dx
+
∫
795. x
x dx
cosh 6
( )
∫
796. x
x dx
csch
2
2
5






∫
797.
csch
coth
1
1
2
2
3
x
x
x
dx












∫
798.
cosh
cosh
ln
ln
x
x
dx
2
2
3
1
−
∫
799.
cosh
sinh
ln
x
x
dx
9
2
0
2
−
∫