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Indian Contributions to the Foundations of Calculus

Description: This quiz will test your knowledge of the contributions made by Indian mathematicians to the foundations of calculus.
Number of Questions: 15
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Tags: indian mathematics calculus history of mathematics
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Which Indian mathematician is credited with developing the concept of the derivative?

  1. Aryabhata

  2. Bhaskara II

  3. Madhava of Sangamagrama

  4. Srinivasa Ramanujan


Correct Option: C
Explanation:

Madhava of Sangamagrama (c. 1340-1425) is credited with developing the concept of the derivative, which is a fundamental concept in calculus.

What is the name of the series used by Madhava of Sangamagrama to approximate the value of pi?

  1. Madhava series

  2. Gregory series

  3. Leibniz series

  4. Taylor series


Correct Option: A
Explanation:

The Madhava series is a series used to approximate the value of pi. It was developed by Madhava of Sangamagrama in the 14th century.

Which Indian mathematician developed the concept of the integral?

  1. Aryabhata

  2. Bhaskara II

  3. Madhava of Sangamagrama

  4. Srinivasa Ramanujan


Correct Option: B
Explanation:

Bhaskara II (1114-1185) developed the concept of the integral, which is another fundamental concept in calculus.

What is the name of the method used by Bhaskara II to calculate the area of a curved surface?

  1. Cavalieri's principle

  2. Exhaustion method

  3. Method of indivisibles

  4. Trapezoidal rule


Correct Option: B
Explanation:

Bhaskara II used the exhaustion method to calculate the area of a curved surface. This method involves dividing the surface into a large number of small pieces and then finding the sum of the areas of these pieces.

Which Indian mathematician developed the concept of the limit?

  1. Aryabhata

  2. Bhaskara II

  3. Madhava of Sangamagrama

  4. Srinivasa Ramanujan


Correct Option: C
Explanation:

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the limit, which is a fundamental concept in calculus.

What is the name of the theorem that states that the derivative of a function is equal to the slope of the tangent line to the graph of the function at a given point?

  1. Rolle's theorem

  2. Mean value theorem

  3. Cauchy's mean value theorem

  4. Taylor's theorem


Correct Option: A
Explanation:

Rolle's theorem states that the derivative of a function is equal to the slope of the tangent line to the graph of the function at a given point.

Which Indian mathematician developed the concept of the chain rule?

  1. Aryabhata

  2. Bhaskara II

  3. Madhava of Sangamagrama

  4. Srinivasa Ramanujan


Correct Option: C
Explanation:

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the chain rule, which is a fundamental concept in calculus.

What is the name of the theorem that states that the integral of a function is equal to the area under the curve of the function?

  1. Fundamental theorem of calculus

  2. Second fundamental theorem of calculus

  3. Mean value theorem

  4. Cauchy's mean value theorem


Correct Option: A
Explanation:

The fundamental theorem of calculus states that the integral of a function is equal to the area under the curve of the function.

Which Indian mathematician developed the concept of the inverse function?

  1. Aryabhata

  2. Bhaskara II

  3. Madhava of Sangamagrama

  4. Srinivasa Ramanujan


Correct Option: C
Explanation:

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the inverse function, which is a fundamental concept in calculus.

What is the name of the theorem that states that the derivative of an inverse function is equal to the reciprocal of the derivative of the original function?

  1. Inverse function theorem

  2. Chain rule

  3. Mean value theorem

  4. Cauchy's mean value theorem


Correct Option: A
Explanation:

The inverse function theorem states that the derivative of an inverse function is equal to the reciprocal of the derivative of the original function.

Which Indian mathematician developed the concept of the logarithmic function?

  1. Aryabhata

  2. Bhaskara II

  3. Madhava of Sangamagrama

  4. Srinivasa Ramanujan


Correct Option: C
Explanation:

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the logarithmic function, which is a fundamental concept in calculus.

What is the name of the theorem that states that the derivative of a logarithmic function is equal to the reciprocal of the function?

  1. Logarithmic differentiation theorem

  2. Chain rule

  3. Mean value theorem

  4. Cauchy's mean value theorem


Correct Option: A
Explanation:

The logarithmic differentiation theorem states that the derivative of a logarithmic function is equal to the reciprocal of the function.

Which Indian mathematician developed the concept of the exponential function?

  1. Aryabhata

  2. Bhaskara II

  3. Madhava of Sangamagrama

  4. Srinivasa Ramanujan


Correct Option: C
Explanation:

Madhava of Sangamagrama (c. 1340-1425) also developed the concept of the exponential function, which is a fundamental concept in calculus.

What is the name of the theorem that states that the derivative of an exponential function is equal to the function itself?

  1. Exponential differentiation theorem

  2. Chain rule

  3. Mean value theorem

  4. Cauchy's mean value theorem


Correct Option: A
Explanation:

The exponential differentiation theorem states that the derivative of an exponential function is equal to the function itself.

Which Indian mathematician developed the concept of the trigonometric functions?

  1. Aryabhata

  2. Bhaskara II

  3. Madhava of Sangamagrama

  4. Srinivasa Ramanujan


Correct Option: A
Explanation:

Aryabhata (476-550) developed the concept of the trigonometric functions, which are fundamental concepts in calculus.

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