L’Hospital’s Rule Practice
x 9 "1
x 5 "1
2. lim+
cos x
1" sin x
e x "1
x!0
x3
4. lim
tan ( px )
tan ( qx )
5. lim
ln x
x!" x
6. lim+
ln x
x
5 x " 3x
7. lim
x!0
x
e x "1" x
8. lim
x!0
x2
1. lim
x!1
x! !2
3. lim
x!0
x!0
ex
x!" x 3
10. lim
1" cos x
x!0
x2
12. lim
x + sin x
x + cos x
x
x!" ln 1+ 2e x
(
)
14. lim
1" x + ln x
1+ cos (! x )
arcsin x
x!0
x
9. lim
11. lim
x!0
13. lim
15. lim
x!1
x a " ax + a "1
( x "1)
2
17. lim cot ( 2x ) sin ( 6x )
x!0
x!1
16. lim+ x ln x
x!0
18. lim+ ln x tan ( !2x )
x!1
Answers
1.
9
5
2. !"
3. !
4.
p
q
5. 0
6. !"
7. ln ( 35 )
8.
1
2
9. !
10. 1
11.
1
2
12. 0
13. 1
14. ! !12
15. 12 a ( a !1)
16. 0
17. 3
18. ! !2