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Questions and Answers
Which branch of mathematics studies continuous change?
Which branch of mathematics studies continuous change?
- Algebra
- Differential calculus (correct)
- Geometry
- Integral calculus
What does differential calculus primarily focus on?
What does differential calculus primarily focus on?
- Instantaneous rates of change (correct)
- Accumulation of quantities
- Areas under or between curves
- Convergence of infinite sequences
What does integral calculus primarily focus on?
What does integral calculus primarily focus on?
- Instantaneous rates of change
- Areas under or between curves
- Accumulation of quantities (correct)
- Convergence of infinite sequences
How are differential calculus and integral calculus related to each other?
How are differential calculus and integral calculus related to each other?
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Who independently developed infinitesimal calculus in the late 17th century?
Who independently developed infinitesimal calculus in the late 17th century?
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Study Notes
Calculus
- Calculus is the branch of mathematics that studies continuous change.
- It is divided into two main branches: differential calculus and integral calculus.
Differential Calculus
- Differential calculus primarily focuses on the study of rates of change and slopes of curves.
- It deals with the derivative of a function, which represents the rate at which the function changes as its input changes.
Integral Calculus
- Integral calculus primarily focuses on the study of accumulation of quantities.
- It deals with the antiderivative of a function, which represents the accumulation of the rates of change of the function over a given interval.
Relationship between Differential and Integral Calculus
- Differential calculus and integral calculus are closely related to each other, as the derivative of a function can be used to find its antiderivative, and vice versa.
- This relationship is known as the Fundamental Theorem of Calculus.
Development of Calculus
- In the late 17th century, Sir Isaac Newton and German mathematician Gottfried Wilhelm Leibniz independently developed infinitesimal calculus.
- They are both credited with the development of calculus, although they used different notations and approaches.
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