Limits

Q. Calculate the limit: lim (x -> 0) (ln(1 + x)/x) (2023)

A. 1
B. 0
C. Undefined
D. Infinity

Solution

Using L'Hôpital's Rule, we differentiate the numerator and denominator to find lim (x -> 0) (1/(1 + x)) = 1.

Correct Answer: A — 1

Learn More →

Q. Calculate the limit: lim (x -> 0) (x^2 sin(1/x))

A. 0
B. 1
C. ∞
D. Undefined

Solution

Since |sin(1/x)| ≤ 1, we have |x^2 sin(1/x)| ≤ |x^2|. Thus, lim (x -> 0) x^2 sin(1/x) = 0.

Correct Answer: A — 0

Learn More →

Q. Calculate the limit: lim (x -> 0) (x^3)/(sin(x)) (2023)

A. 0
B. 1
C. ∞
D. Undefined

Solution

Using the fact that sin(x) ~ x as x approaches 0, we find that lim (x -> 0) (x^3)/(sin(x)) = 0.

Correct Answer: A — 0

Learn More →

Q. Calculate the limit: lim (x -> 2) (x^3 - 8)/(x - 2)

A. 4
B. 8
C. 6
D. 2

Solution

Factoring gives lim (x -> 2) ((x - 2)(x^2 + 2x + 4))/(x - 2) = lim (x -> 2) (x^2 + 2x + 4) = 12.

Correct Answer: A — 4

Learn More →

Q. Calculate the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4) (2023)

A. 3/5
B. 0
C. 1
D. ∞

Solution

Dividing numerator and denominator by x^2 gives lim (x -> ∞) (3 + 2/x^2)/(5 - 4/x^2) = 3/5.

Correct Answer: A — 3/5

Learn More →

Q. Calculate the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4x + 1) (2023)

A. 3/5
B. 5/3
C. 1
D. 0

Solution

Dividing numerator and denominator by x^2 gives lim (x -> ∞) (3 + 2/x^2)/(5 - 4/x + 1/x^2) = 3/5.

Correct Answer: A — 3/5

Learn More →

Q. Find the limit: lim (x -> 0) (x^3)/(sin(x)) (2023)

A. 0
B. 1
C. Infinity
D. Undefined

Solution

Using the fact that sin(x) approaches x as x approaches 0, we have lim (x -> 0) (x^3)/(sin(x)) = 0.

Correct Answer: A — 0

Learn More →

Q. Find the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4x + 1)

A. 3/5
B. 0
C. 1
D. Infinity

Solution

As x approaches infinity, the leading terms dominate. Thus, lim (x -> ∞) (3x^2)/(5x^2) = 3/5.

Correct Answer: A — 3/5

Learn More →

Q. What is the limit: lim (x -> 0) (1 - cos(x))/(x^2)? (2022)

A. 0
B. 1/2
C. 1
D. Undefined

Solution

Using the identity 1 - cos(x) = 2sin^2(x/2), we have lim (x -> 0) (1 - cos(x))/(x^2) = lim (x -> 0) (2sin^2(x/2))/(x^2) = 1/2.

Correct Answer: B — 1/2

Learn More →

Q. What is the limit: lim (x -> 0) (cos(x) - 1)/x^2? (2019)

A. 0
B. -1/2
C. 1
D. Undefined

Solution

Using the Taylor series expansion for cos(x), we find that lim (x -> 0) (cos(x) - 1)/x^2 = -1/2.

Correct Answer: B — -1/2

Learn More →

Q. What is the limit: lim (x -> 0) (e^x - 1)/x? (2022)

A. 1
B. 0
C. e
D. Undefined

Solution

Using the derivative of e^x at x = 0, we find that lim (x -> 0) (e^x - 1)/x = 1.

Correct Answer: A — 1

Learn More →

Q. What is the limit: lim (x -> 0) (ln(1 + x)/x)?

A. 1
B. 0
C. ∞
D. Undefined

Solution

Using L'Hôpital's Rule, we differentiate the numerator and denominator to find lim (x -> 0) (1/(1 + x)) = 1.

Correct Answer: A — 1

Learn More →

Q. What is the limit: lim (x -> 0) (tan(3x)/x)?

A. 3
B. 0
C. 1
D. Infinity

Solution

Using the limit lim (x -> 0) (tan(x)/x) = 1, we have lim (x -> 0) (tan(3x)/x) = 3 * lim (x -> 0) (tan(3x)/(3x)) = 3.

Correct Answer: A — 3

Learn More →

Q. What is the limit: lim (x -> 1) (x^2 - 1)/(x - 1)? (2019)

A. 0
B. 1
C. 2
D. Undefined

Solution

Factoring gives (x - 1)(x + 1)/(x - 1), which simplifies to x + 1. Thus, lim (x -> 1) (x + 1) = 2.

Correct Answer: C — 2

Learn More →

Showing 1 to 14 of 14 (1 Pages)

Limits MCQ & Objective Questions

Understanding "Limits" is crucial for students preparing for various exams in India. This fundamental concept lays the groundwork for calculus and is frequently tested in both school and competitive exams. Practicing MCQs and objective questions on Limits not only enhances your grasp of the topic but also boosts your confidence, helping you score better in your exams.

What You Will Practise Here

Definition and basic concepts of Limits
Types of Limits: Finite and Infinite
Limit laws and properties
Finding Limits using algebraic methods
Understanding one-sided limits
Application of Limits in real-world problems
Graphical interpretation of Limits

Exam Relevance

The topic of Limits is a significant part of the syllabus for CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to apply limit laws, evaluate limits using different methods, and interpret graphical representations. Common question patterns include direct computation of limits, application-based scenarios, and conceptual understanding through multiple-choice questions.

Common Mistakes Students Make

Confusing one-sided limits with two-sided limits
Neglecting to simplify expressions before finding limits
Misapplying limit laws in complex problems
Overlooking the importance of continuity in relation to limits

FAQs

Question: What are Limits in mathematics?
Answer: Limits describe the value that a function approaches as the input approaches a certain point.

Question: How can I improve my understanding of Limits?
Answer: Regular practice of Limits MCQ questions and reviewing important concepts will enhance your understanding significantly.

Now is the time to take charge of your exam preparation! Dive into our practice MCQs on Limits and test your understanding. Every question you solve brings you one step closer to mastering this essential topic.

Limits

Limits MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?