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Functions and limits

5 Class 12 Mathematics questions with answers and explanations.

Printable worksheet with answer key

All questions with answers
  1. The limit of (x2 - 1) / (x - 1) as x tends to 1 is:

    • 1 0
    • 2 2
    • 3 Does not exist
    • 4 1
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    Correct answer: 2

    (x + 1)(x - 1) / (x - 1) = x + 1, which tends to 2.

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  2. The limit of sin x / x as x tends to 0 is:

    • 1 1
    • 2 -1
    • 3 Infinity
    • 4 0
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    Correct answer: 1

    This is a standard limit equal to 1.

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  3. The limit of (3x + 2) as x tends to 2 is:

    • 1 6
    • 2 2
    • 3 4
    • 4 8
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    Correct answer: 8

    Substitute x = 2: 6 + 2 = 8.

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  4. A function f is continuous at x = a if the limit as x tends to a equals:

    • 1 a
    • 2 f(a)
    • 3 1
    • 4 0
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    Correct answer: f(a)

    Continuity needs the limit to equal the function's value.

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  5. The limit of (1 + 1/n)^n as n tends to infinity is:

    • 1 1
    • 2 Infinity
    • 3 0
    • 4 e
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    Correct answer: e

    This is the definition of the number e.

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