Chapter Exam

Chapter-12 Limits and Derivatives — Online MCQ Test

Q: What is the left-hand limit of a function f(x) at x = a denoted as?

Answer: B. lim(x→a⁻) f(x) — The left-hand limit is denoted by lim(x→a⁻) f(x), which means x approaches a from values less than a.

Q: For a limit to exist at x = a, which condition must be satisfied?

Answer: C. Left-hand limit = Right-hand limit — For a limit to exist at x = a, the left-hand limit and right-hand limit must be equal: lim(x→a⁻) f(x) = lim(x→a⁺) f(x).

Q: Find lim(x→2) (x² + 3x + 2):

Answer: A. 12 — By direct substitution: lim(x→2) (x² + 3x + 2) = 2² + 3(2) + 2 = 4 + 6 + 2 = 12.

Q: Given f'(x) = 3x² and f(1) = 2, which statement about f is true?

Answer: A. f(x) = x³ + 1 — If f'(x) = 3x², then f(x) = x³ + c. Using f(1) = 2: 1³ + c = 2, so c = 1, giving f(x) = x³ + 1.

MATHS · Grade 11 · CBSE(NCERT)

Practice Chapter-12 Limits and Derivatives with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 11 MATHS. This chapter covers: Left-hand limit - Right-hand limit - Existence of limit - Algebra of limits - Standard limits - Derivative - Rate of change - First principle - Product rule - Quotient rule. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-12 Limits and Derivatives — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 11 MATHS — Chapter-12 Limits and Derivatives, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the left-hand limit of a function f(x) at x = a denoted as?

A. lim(x→a⁺) f(x)
B. lim(x→a⁻) f(x) ✓
C. lim(x→a) f(x)
D. lim(x→0) f(x)

Answer: B. lim(x→a⁻) f(x)
The left-hand limit is denoted by lim(x→a⁻) f(x), which means x approaches a from values less than a.

For a limit to exist at x = a, which condition must be satisfied?

A. Only left-hand limit should exist
B. Only right-hand limit should exist
C. Left-hand limit = Right-hand limit ✓
D. Either left or right-hand limit should exist

Answer: C. Left-hand limit = Right-hand limit
For a limit to exist at x = a, the left-hand limit and right-hand limit must be equal: lim(x→a⁻) f(x) = lim(x→a⁺) f(x).

Find lim(x→2) (x² + 3x + 2):

A. 12 ✓
B. 10
C. 8
D. 14

Answer: A. 12
By direct substitution: lim(x→2) (x² + 3x + 2) = 2² + 3(2) + 2 = 4 + 6 + 2 = 12.

If f(x) = |x| at x = 0, which statement is true?

A. Left-hand limit = 0 and Right-hand limit = 0, limit exists ✓
B. Left-hand limit ≠ Right-hand limit, limit does not exist
C. Only left-hand limit exists
D. The function is differentiable at x = 0

Answer: A. Left-hand limit = 0 and Right-hand limit = 0, limit exists
For f(x) = |x|: lim(x→0⁻) |x| = 0 and lim(x→0⁺) |x| = 0, so the limit exists and equals 0. However, the function is not differentiable at x = 0.

Given f'(x) = 3x² and f(1) = 2, which statement about f is true?