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Calculus Study: Differential and Integral Calculus
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Calculus Study: Differential and Integral Calculus

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Questions and Answers

What are the two major branches of calculus?

  • Differential calculus and algebraic calculus
  • Algebraic calculus and geometric calculus
  • Geometric calculus and arithmetic calculus
  • Differential calculus and integral calculus (correct)
  • Who independently developed infinitesimal calculus in the late 17th century?

  • Isaac Newton and Albert Einstein
  • Albert Einstein and Gottfried Wilhelm Leibniz
  • Isaac Newton and Carl Friedrich Gauss
  • Gottfried Wilhelm Leibniz and Isaac Newton (correct)
  • What fundamental notions are used by the two branches of calculus to relate to each other?

  • Fundamental theorem of algebra
  • Fundamental theorem of trigonometry
  • Fundamental theorem of calculus (correct)
  • Fundamental theorem of geometry
  • What does the word 'calculus' mean in Latin?

    <p>Small pebble</p> Signup and view all the answers

    In mathematics education, what does calculus denote?

    <p>Courses of elementary mathematical analysis</p> Signup and view all the answers

    Who developed modern calculus independently of each other?

    <p>Isaac Newton and Gottfried Wilhelm Leibniz</p> Signup and view all the answers

    Which ancient mathematician developed the method of exhaustion to prove formulas for cone and pyramid volumes?

    <p>Eudoxus of Cnidus</p> Signup and view all the answers

    In which ancient culture was the method of exhaustion discovered independently to find the area of a circle?

    <p>China</p> Signup and view all the answers

    Who derived a formula for the sum of fourth powers in the Middle East?

    <p>Hasan Ibn al-Haytham</p> Signup and view all the answers

    Which ancient mathematician combined the method of exhaustion with a concept of the indivisibles?

    <p>Archimedes</p> Signup and view all the answers

    Which mathematician developed the concept of limits, putting the development of infinitesimal calculus on a more solid conceptual footing?

    <p>Archimedes</p> Signup and view all the answers

    What did Leibniz originally call the mathematical study of continuous change?

    <p>Integral calculus</p> Signup and view all the answers

    Which ancient culture discovered the method of exhaustion independently to find the area of a circle?

    <p>Egyptian</p> Signup and view all the answers

    Who combined the method of exhaustion with a concept of the indivisibles in ancient mathematics?

    <p>Euclid</p> Signup and view all the answers

    What ancient mathematician developed the method of exhaustion to prove formulas for cone and pyramid volumes?

    <p>Eudoxus</p> Signup and view all the answers

    Who is credited with developing modern calculus independently of each other?

    <p>Gottfried Wilhelm Leibniz</p> Signup and view all the answers

    In which ancient culture was the method of exhaustion discovered independently to find the area of a circle?

    <p>China</p> Signup and view all the answers

    Which ancient mathematician combined the method of exhaustion with a concept of the indivisibles, a precursor to infinitesimals?

    <p>Archimedes</p> Signup and view all the answers

    Who derived a formula for the sum of fourth powers in the Middle East?

    <p>Alhazen</p> Signup and view all the answers

    Which ancient Greek mathematician developed the method of exhaustion to prove the formulas for cone and pyramid volumes?

    <p>Eudoxus of Cnidus</p> Signup and view all the answers

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