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

In mathematics education, what does calculus denote?

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

Who developed modern calculus independently of each other?

<p>Isaac Newton and Gottfried Wilhelm Leibniz (C)</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 (D)</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 (B)</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 (D)</p> Signup and view all the answers

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

<p>Archimedes (A)</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 (B)</p> Signup and view all the answers

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

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

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

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

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

<p>Gottfried Wilhelm Leibniz (B)</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 (D)</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 (C)</p> Signup and view all the answers

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

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

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