4.3 The Limit of Indeterminate Forms and L’Hospital’s Rule
by SGLee - HSKim -JHLee
1-11. Evaluate the limits of the given indeterminate forms.
1. 
Apply L'Hospital Rule twice.
Calculus-Sec-4-3-Solution
4.3 The Limit of Indeterminate Forms and L’Hospital’s Rule
by SGLee - HSKim -JHLee
1-11. Evaluate the limits of the given indeterminate forms.
1.
Apply L'Hospital Rule twice.
2. 
3. 
By L'Hospital Rule, 
.
4. 
5. 
Let 
. Note 
and 
. By L`Hospital’s Rule,
(
)
.
7. 
1
8. 
By L'Hospital’s Rule
.
9. 
11. 
.
12. Let 
. Use L'Hospital's Theorem to show that 
. <-- x가 +infinity로 가야 함 (수정 필요)
, since 
is constant and the denominator grows without bound.
13. For what values of 
and 
is the following equation correct?
By L'Hospital’s Rule for a form of type 
and we may take 
to be any value.
15. 
. Note 
Therefore, by L’Hospital’s Rule,
.
16-17. Find the following limit.
16. 
(by L'Hospital’s Rule) or 
.
17. 
(by L'Hospital’s Theorem)
or 
.
18-27. Find the limit by using L'Hospital's rule. If you cannot apply L'Hospital's rule, explain why and then find the limit by another method.
18. 
, limit does not exists.
20. 
Apply L'Hospital's rule, 
22. 
23. 
24. 
does not exist.
25. 
27. 
28. The function 
is defined by
and 
.
Answer the following questions.
(a) Find 
.
(b) Does 
exist?
(a) 
(b) 
does not exist.
29. Let 
be a continuous function with 
and 
. Find 
.
and 
. Hence, by L'Hospital’s Theorem
.
30. Let 
be the angle of a sector of a circle. Find 
where 
and 
are
the area of the segment shaded region between the chord 
and arc
, the area of the triangle 
respectively.
,
.
6. 
10. 
.
by L'Hospital Rule for a form of type 
(by L`Hospital`s Rule) 
.
21. 
26. 
