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Calculus Basics

Limits, differentiation, integration, and applications of derivatives

Sample Practice Questions

  1. The quotient rule: d/dx [u/v] =

    • u'v'
    • (u'v - uv')/v²
    • (v·u' - u·v')/v²
    • u'/v - u/v²
    Show answer

    Answer: (v·u' - u·v')/v²

  2. Implicit differentiation: if x² + y² = 25, then dy/dx =

    • x/y
    • -x/y
    • y/x
    • -y/x
    Show answer

    Answer: -x/y

  3. If f'(x) = 0 and f''(x) = 0 at x = a, then x = a is likely:

    • A maximum
    • A minimum
    • An inflection point
    • A discontinuity
    Show answer

    Answer: An inflection point

  4. What is the derivative of e^x?

    • xe^(x-1)
    • e^x
    • e^(x-1)
    • xe^x
    Show answer

    Answer: e^x

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Practice Questions

Practise NMO questions on Calculus Basics. Answers are revealed after each question.

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