Class 11 Mathematics · Chapter 12 · Test 1
Limits of Functions
45 MCQs Covers limit theorems, limits of sequences, and algebraic limits including rationalization and factoring.
45 questions · 40 min · 45 marks
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Sample questions
The first 5 of 45. Try each one, then tap to see the answer.
Question 1
The limit of f(x) as x approaches a is L means that:
- Af(a) must equal L
- Bf(x) gets arbitrarily close to L as x approaches a from both sides
- Cf(x) is always greater than L near a
- Dx must equal a
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Answer: B
lim f(x) = L describes the behaviour of f near a (from left and right); f need not even be defined at a.
Question 2
If lim f(x) = L and lim g(x) = M as x → a, then lim [f(x) + g(x)] equals:
- AL·M
- BL − M
- CL/M
- DL + M
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Answer: D
The limit of a sum is the sum of the limits.
Question 3
If lim f(x) = L as x → a and k is a constant, then lim [k f(x)] equals:
- AkL
- BL + k
- CL/k
- Dk + f(a)
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Answer: A
A constant factor can be taken outside the limit.
Question 4
If lim f(x) = L and lim g(x) = M, then lim f(x)·g(x) equals:
- AL + M
- BL/M
- CL·M
- DL − M
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Answer: C
The limit of a product is the product of the limits.
Question 5
The limit of a quotient lim f(x)/g(x) equals L/M provided that:
- AL ≠ 0
- BM ≠ 0
- CL = M
- DM = 0
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Answer: B
The limit of the denominator must be non-zero.
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