2. Consider the function below and investigate on the values of π(π₯) for
the given values of π₯.
π π =
ππ
β ππ
π β π
Table A Table B
8. Consider a function f(π). Consider a constant π which the
variable π will approach (π may or may not be in the domain
of π).
The limit, to be denoted by π³, is the unique real value that π(
π) will approach as π approaches π. In symbols, we write this
process as
This is read as βThe limit of π(π) as π approaches π is π³.β
π₯π’π¦
πβπ
π π = π³
14. The limit is the unique real
value that π(π) will approach
as π approaches π.
π₯π’π¦
πβπ
π π = π³
π₯π’π¦
πβπβ
π π π₯π’π¦
πβπ+
π π
Left-hand Limit Right-hand
Limit
Judgment:
ο± If both left-hand and right-
hand limits are EQUAL,
the limit exist, which is L
(value).
ο± If both left-hand and right-
hand limits are NOT
EQUAL, the limit does not
exist (DNE).
15. π π = π + ππ
π₯π’π¦
πβπ
π π = π³ π₯π’π¦
πβπ
(π + ππ) = π³
Find the limit of the function, as x approaches 2.
π₯π’π¦
πβπβ
(π + ππ) = π³ π₯π’π¦
πβπ+
(π + ππ) = π³
βThe limit of f(x) as x approaches
2 from the leftβ
βThe limit of f(x) as x approaches
2 from the rightβ
19. Using the graph, find the limit of the function as x
approaches from the following values.
1. π₯ = β1
2. π₯ = 3
3. π₯ = β3.75
4. π₯ = 1
5. π₯ = 5
20. 1. Form a circle with your group mates.
2. Prepare your pens and calculators.
3. As you received the material from the
teacher, provide the necessary answer.
4. If you are already done answering, give
the material to the teacher.
5. Prepare your group for a presentation
later.
23. Directions: Get 1 whole yellow paper per group. Copy
and answer only. Do not include the graph in your
paper.
A. Construct two tables of values to find the .
B. Consider the function π(π₯) whose graph is given below.
1.
2.
3.
4.
5.
lim
π₯β1
(π₯3
+2π₯)
lim
π₯ββ3
π π₯ =
lim
π₯β1
π π₯ =
lim
π₯β3
π π₯ =
lim
π₯β2
π π₯ =
lim
π₯β4
π π₯ =
24. Directions: Get 1 whole yellow paper per group. Copy
and answer only. Do not include the graph in your
paper.
A. Construct two tables of values to
find the
B. Consider the function π(π₯) whose
graph is given below.
1.
2.
3.
4.
5.
lim
π₯β1
(π₯3+2π₯)
lim
π₯ββ3
π π₯ =
lim
π₯β1
π π₯ =
lim
π₯β2
π π₯ =
lim
π₯β6
π π₯ =
lim
π₯β4
π π₯ =
25. Arceo, Carlene Perpetua P., Richard S. Lemence, Oreste Jr. M. Ortega, and Louie John D.
Vallejo. (2016). Teaching Guide For Senior High School Basic Calculus. Diliman,
Quezon City: Comission on Higher Education
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