math

1. DESIGNER Ms. Mery Ann M. Alday WEEK NO. /DATE Week 3 – Jan. 15-19, 2024
SUBJECT Mathematics GRADE LEVEL Grade 11
MELCs:
TRANSFER GOAL:
FORMATION
STANDARD:
TOPIC/s
Evaluating the Limits of Algebraic Functions
LEARNING OBJECTIVE
 Evaluate left and right hand
MOTIVATION
Entry Card
Evaluate the following Limits
1. lim
𝑥→9
𝑥2
2. lim
𝑥→4
6𝑥
𝑥−2
INTERACT
In-depth discussion of the lesson
If n is any positive integer and lim
𝑥→𝑎
𝑓(𝑥) = 𝐿,
𝑡ℎ𝑒𝑛lim √𝑓(𝑥)
𝑛
= √𝐿
𝑛
𝑥→𝑎
lim
𝑥→3
√8𝑥 + 3
3
=?
1. lim
𝑥→3
4𝑥 =?
2. lim
𝑥→2
3𝑥 − 9 =?
3. lim
𝑥→0
𝑥(3𝑥 + 1)
4. lim
𝑥→5
𝑥
2
?
5. lim
𝑥→0
𝑥3
=?
lim
𝑥→2
(
𝑥 − 2
𝑥2 − 4
) =?
lim
𝑥→3
(
𝑥 − 2
𝑥2 − 3𝑥 + 2
) =?
The limit of a function is called two-sided limit if it requires the values of f(x) to get closer and closer to a
number as the values of x are taken from either side of x=a. However some functions exhibit different
behaviors on the two sides of an x-value a in which case it is necessary to distinguish whether the values of x
near a are on the left side or on the right side of a for purposes of investigating limiting behavior.

2. For the functions in Fig 1.1.13, find the one-sided limit and the two-sided limits at x=a if they exists.
SOLUTION
The functions in all three figures have the same one-sided limits as x ® a
, since the functions are Identical,
except at x=a.
These lim its are
lim f ( x ) = 3 and lim f ( x ) = 1
x®a+
x®a-
In all three cases the two-sided limit does not exist as
x ® a
because the one sided limits are not equal.
INVOLVE
INTEGRATE
. Formulate your own if-then statement in promoting
The Lady Mediatrix Institute.
INTELECTUALIZE
Underline the hypothesis, then circle the conclusion.

3. 1. If you are born in the Philippines, then you are a Filipino.
2. If it rains, then the ground is wet.
3. If a person is rich, then she can buy what she wants.
4. If a person is color blind, then he has color vision deficiency.
5. If the person has acrophobia, then he has fear of heights.
6. If there are two points, then a line can be drawn.
7. If two distinct lines intersect, their intersection is a point.
8. If today is Tuesday, then tomorrow is Wednesday.
9. If you are honest, then you do not lie.
10. If a polygon has five sides, then it is a pentagon.
REMARKS