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Gunadarma Searching & Sorting Algorithm Quiz, Quizzes of Algorithms and Programming

10 Question quiz about searching and sorting algorithm

Typology: Quizzes

2023/2024

Available from 06/02/2024

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Gunadarma University
Subject : Basic Mathematics
Faculty : Industrial Technology
Program of Study : Informatics Engineering Major
Years : 2024
Calculus Practice Quiz
1. Evaluate the limit : lim
x→2
𝑥2 - 4
x - 2 .
A) 2
B) 4
C) 0
D) 8
Explanation:
lim
x→2
𝑥2 - 4
x - 2 = lim
x→2
(x - 2)(x + 2)
x - 2 = lim
x→2(x + 2) = 2 + 2 = 4
2. Determine if the following limit exists: lim
x→0
sin(x)
x.
A) 0
B) 1
C) Does not exist
D) 1
Explanation: This is a standard limit. By applying L'Hôpital's Rule or knowing the special limit:
lim
x→0
sin(x)
x = 1
pf3
pf4

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Gunadarma University

Subject : Basic Mathematics

Faculty : Industrial Technology

Program of Study : Informatics Engineering Major

Years : 2024

Calculus Practice Quiz

1. Evaluate the limit : lim

x→ 2

𝑥

2

  • 4

x - 2

A) 2

B) 4

C) 0

D) 8

Explanation:

lim

x→ 2

𝑥

2

  • 4

x - 2

= lim

x→ 2

(x - 2 )(x + 2 )

x - 2

= lim

x→ 2

(x + 2 ) = 2 + 2 = 4

2. Determine if the following limit exists: lim

x→ 0

sin(x)

x

A) 0

B) 1

C) Does not exist

D) − 1

Explanation: This is a standard limit. By applying L'Hôpital's Rule or knowing the special limit:

lim

x→ 0

sin(x)

x

3. Find the limit: lim

x→∞

3 𝑥

2

  • 2 𝑥+ 1

𝑥

2

−𝑥+ 4

A) 1

B) 2

C) 3

D) 0

Explanation: Divide the numerator and denominator by x

2

lim

x→∞

3 +

2

x

1

𝑥

2

1 -

1

x

4

𝑥

2

3 + 0 + 0

1 - 0 + 0

  1. Evaluate the limit: lim

𝑥→ 0

A) −∞

B) 0

C) ∞

D) Does not exist

Explanation: As xxx approaches 000 from the positive side, the natural logarithm function goes

to −∞:

lim

𝑥→ 0

  1. Find the derivative of the function: f(x) = 3x

4

− 5x

3

  • 2x − 7.

A) 12x

3

− 15x

2

B) 12x

3

− 10x

2

C) 12x

4

− 15x

3

D) 12x

3

− 15x + 2

Explanation: Using logarithmic differentiation:

y = x

2

⟹ ln(y) = x ln(x) ⟹

1

y

dy

dx

= ln(x) + 1 ⟹

dy

dx

= y(ln(x) + 1) = x

2

  1. Find the critical points of the function f(x) = x

3

− 3x

2

A) x = 0

B) x = 2

C) x = 1

D) x = − 1

Explanation: Set the derivative equal to zero:

f′(x) = 3x

2

− 6x = 3x(x − 2) = 0 ⟹ x = 0 or x = 2

The critical point in the given options is x=1x = 1x= 1.

  1. Determine the intervals on which f(x) =

1

𝑥

2

  • 1

is increasing or decreasing.

A) Increasing on (−∞, −1) ∪ (1, ∞), decreasing on (−1, 1)

B) Increasing on (−1, 1), decreasing on (−∞, −1) ∪ (1, ∞)

C) Increasing on (−∞, ∞)

D) Decreasing on (−∞, ∞)

Explanation: Compute the derivative:

f′(x) = -

2x

(𝑥

2

  • 1 )

2

Analyze the sign of f′(x):

o f′(x) > 0 when − 1 < x < 1

o f′(x) < 0 when x < −1x or x > 1