WorksheetsCALCULUS Midterm Examination for BSIT
Total questions: 20
Worksheet time: 5hrs 0mins
Name
Class
Date
1.
It is the mathematical tool that is used to study how things change and the rate at which they change.
a)
Integral Calculus
b)
Algebra
c)
Differential Calculus
d)
Calculus
2.
Limit theorem 5 states that the limit of a product is the product of the limits.
a)
True
b)
False
3.
Evaluate limit √x2 +8.
x→1
x→1
a)
9
b)
3
c)
8
d)
4
4.
Evaluate lim (3x4 - 2x3 + 4x +3).
x→3
x→3
a)
198
b)
199
c)
203
d)
204
5.
Find the derivative of f(x)=x.
a)
x
b)
1
c)
2
d)
3
6.
Find the derivative of f(x) = x3 +2x2 -1.
a)
3x2 - 4x
b)
-3x2 - 4x
c)
-3x2 + 4x
d)
3x2 + 4x
7.
Find the derivative of f(x)=3x+5.
a)
8
b)
5
c)
3
d)
3x
8.
Find the derivative of the quotient if y= x2+ 3x +4 / x+3.
a)
x2-5/(x+3)2
b)
-x2-5/(x+3)2
c)
x2+5/(x+3)2
d)
-x2+5/(x+
9.
Evaluate limit √x2 + 16 as x approaches to 3.
a)
7
b)
5
c)
9
d)
10
10.
Find the derivative of the product if y= (x2 -3)(2x3 + 1), then y′ = uv′+ vu′.
a)
10x4- 18x2 -2x
b)
10x4+ 18x2 +2x
c)
10x4 +18x2 -2x
d)
10x4- 18x2 +2x
11.
Find the derivative of f(x)= 2x2( x3 -4) by calculating lim f(x+ Δx)- f(x)/Δx.
Δx→0
Δx→0
a)
10x4 -16x
b)
10x4 +16x
c)
16x4 -10x
d)
16x4 +10x
12.
Isaac Newton from Germany and Gottfried Wilhelm Leibniz from England discovered and developed Calculus?
a)
True
b)
False
13.
Differential Calculus: Rate of Change and Integral Calculus: Accumulation.
a)
False
b)
True
14.
The function f(x)= x2 + 2x is continuous is at x= 1.
a)
True
b)
False
15.
If one or more of the three conditions fails to hold at a , then the function is said to be _______________ at a.
a)
Continuous
b)
Discontinuous
c)
Continuity
d)
Undefined
16.
Given f(x)= x2 -4/ x-2 is continuous at x=2.
a)
True
b)
False
17.
Which of the following statement is true?
a)
The function approaches a limit as x approaches a, that is limit f(x) exists then it is continuous.
b)
The function approaches a limit as x approaches a, that is limit f(x) exists ,then it is discontinuous.
c)
The function approaches x limit as x approaches a, that is limit f(x) exists then it is continuous.
d)
The function approaches x limit as x approaches a, that is limit f(x) exists, then it is discontinuous.
18.
The limit of x-1/x2 as x approaches to 1 is undefined.
a)
False
b)
True
19.
Evaluate lim f(x)- f(a)/ x-a as x approaches to a. If f(x) = 1-2x2 and a =3.
a)
6
b)
-6
c)
12
d)
-12
20.
The function f(x)= 2/(3x+1)(x+2) is continuous.
a)
False
b)
True
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