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 (D)</p> Signup and view all the answers

Which fundamental theorem relates differential calculus and integral calculus?

<p>Fundamental Theorem of Calculus (A)</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 (D)</p> Signup and view all the answers

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

<p>Johann Bernoulli (A)</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 (D)</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 (D)</p> Signup and view all the answers

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

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