Republic of the Philippines
Department of Education
NATIONAL CAPITAL REGION
Name: _________________________________ Grade & Section: ____________________ Score: ________
Teacher: _______________________ Parent’s Name & Signature: ____________________ Date: _________
MONTHLY EXAMINATION
BASIC CALCULUS – GRADE 11
Second Semester – Third Quarter
School Year 2025 – 2026
I. Multiple Choice: Read each item carefully. Write
the LETTER of the BEST answer before each item.
_____ 2) Given lim (1 + 3𝑥) ,what is the value of c?
A.
This
says
that
the
limit
of a sum of functions is the sum of the limits of the
individual functions.
B. This says that the limit of a sum of functions is the
difference of the limits of the individual functions.
C. This says that the limit of a sum of functions is the
product of the limits of the individual functions.
D. This says that the limit of a sum of functions is 0.
A.2
B. x
_____ 8) Which of the following describes the
equation below?
_____ 1) Which of the following is true about the limit
of a function?
A. The limit of a function always exists.
B. The limit of a function f(x) exists if and only if the
one sided limits of the function are equal.
C.The limit of a function will never exist
D.The limit of a function is always equal to 1.
𝑥→2
C.1+3x
D. 7
_____ 3) Which of the following values of x can make
2𝑥+1
the function 𝑓(𝑥) = 2𝑥−4 undefined?
A. 0
B. 1
C. 2
D.3
_____ 4) What is the lim 789
𝑥→𝑐
A. C
B. 0
C. 789
D. DNE
A. This says that the limit of a sum of functions is the
sum of the limits of the individual functions.
B. This says that the limit of a difference of functions
is the difference of the limits of the individual functions.
C. This says that the limit of a product of functions is
the product of the limits of the individual functions.
D. This says that the limit of a sum of functions is 0.
_____ 9) Given the table of values below, what is
lim (1 + 3𝑥)?
𝑥→2
_____ 5)Given 𝑔(𝑥) = 𝑥 3 − 2, find f(3)?
A. 27
B. -27
C. 25
D. -25
_____ 6)Which of the following is true about the limit
of a constant?
A. The limit of a constant is always equal to 0.
B. The limit of a constant is always equal to 1.
C. The limit of a constant is itself.
D. The limit of a constant does not exist
_____ 7) Which of the following describes the
equation below?
A. 0
B. 7
C. 2
D. 10
_____ 10) Evaluate the
by looking at
its graph
1
III. Consider the function f(x) whose graph is
shown below.
A. 0
C.1
D.DNE
B.+∞
II. True or False. Write A if the statement is True
and B if False.
11) 𝑙𝑖𝑚 𝑓(𝑥) = 𝐿 is read as the limit of f(x) as x
𝑥→𝑐
approaches c is L.
Graph of y = f (x)
12) If the 𝑙𝑖𝑚− 𝑓(𝑥) ≠ 𝑙𝑖𝑚+ 𝑓(𝑥), then 𝑙𝑖𝑚 𝑓(𝑥) = L.
𝑥→𝑐
𝑥→𝑐
𝑥→𝑐
13) The values approaching from the right of a number
are the values greater than that number.
14) The Division Theorem states that the limit of a
quotient of functions is equal to the quotient of the
limits of the individual functions, provided the
denominator limit is equal to 0.
15) lim 1 = 0
𝑥→0
16) The limit of the given function does not exist if the
limit from the left and right side are not equal.
Determine the following
A. 17-18)
19-20)
21-22)
𝑙𝑖𝑚
𝑓(𝑥) = __________
𝑙𝑖𝑚
𝑓(𝑥) = __________
𝑙𝑖𝑚
𝑓(𝑥) = __________
𝑥→−1.5−
𝑥→−1.5+
𝑥→−1.5
B. 23-24) 𝑙𝑖𝑚− 𝑓(𝑥) = __________
𝑥→0
25-26)
𝑙𝑖𝑚+ 𝑓(𝑥) = __________
27-28)
𝑙𝑖𝑚 𝑓(𝑥) = __________
C. 29-30)
𝑥→0
𝑥→0
𝑙𝑖𝑚 𝑓(𝑥) = __________
𝑥→2−
31-32)
𝑙𝑖𝑚+ 𝑓(𝑥) = __________
33-34)
𝑙𝑖𝑚 𝑓(𝑥) = __________
D. 35-36)
𝑙𝑖𝑚 − 𝑓(𝑥) = __________
37-38)
39-40)
𝑥→2
𝑥→2
𝑥→4
𝑙𝑖𝑚 𝑓(𝑥) = __________
𝑥→4 +
𝑙𝑖𝑚 𝑓(𝑥) = __________
𝑥→4
2