Calculus Basics
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Questions and Answers

What are the two major branches of calculus?

  • Differential calculus and integral calculus (correct)
  • Integral calculus and algebraic calculus
  • Algebraic calculus and limit calculus
  • Differential calculus and algebraic calculus

    • Who developed infinitesimal calculus independently in the late 17th century?

  • Isaac Newton and Carl Friedrich Gauss
  • Gottfried Wilhelm Leibniz and Carl Friedrich Gauss
  • Isaac Newton and Albert Einstein
  • Isaac Newton and Gottfried Wilhelm Leibniz (correct)

    • What is the Latin meaning of the word 'calculus'?

  • Big stone
  • Infinite sequence
  • Small pebble (correct)
  • Mathematical computation

    • What does differential calculus primarily concern?

    <p>Instantaneous rates of change</p> Signup and view all the answers

    Which fundamental theorem relates differential calculus and integral calculus?

    <p>Fundamental Theorem of Calculus</p> Signup and view all the answers

    What is L'Hôpital's rule?

    <p>A mathematical theorem for evaluating limits of indeterminate forms using derivatives</p> Signup and view all the answers

    Who first introduced L'Hôpital's rule to Guillaume de l'Hôpital?

    <p>Johann Bernoulli</p> Signup and view all the answers

    Under what conditions does L'Hôpital's rule apply?

    <p>When the quotient of the derivatives of f(x) and g(x) exists as a limit at x=c</p> Signup and view all the answers

    What role does differentiation play in L'Hôpital's rule?

    <p>It simplifies the quotient or converts it to a limit that can be evaluated directly</p> Signup and view all the answers

    What does L'Hôpital's rule allow for evaluating?

    <p>Limits of indeterminate forms using derivatives</p> Signup and view all the answers

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