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Madhava's Contributions to Calculus and Infinite Series

Description: Madhava's Contributions to Calculus and Infinite Series
Number of Questions: 15
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Tags: indian mathematics classical indian mathematics texts calculus infinite series
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Who is considered to be the founder of the Kerala school of astronomy and mathematics?

  1. Madhava of Sangamagrama

  2. Aryabhata

  3. Bhaskara II

  4. Brahmagupta

Show answer
Correct Option: A
Explanation:

Madhava of Sangamagrama is credited with founding the Kerala school of astronomy and mathematics in the 14th century.

What is the name of the series that Madhava used to approximate the sine function?

  1. Madhava series

  2. Taylor series

  3. Fourier series

  4. Maclaurin series

Show answer
Correct Option: A
Explanation:

The Madhava series is a series expansion for the sine function that was discovered by Madhava of Sangamagrama.

What is the general formula for the Madhava series?

  1. $$\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$$

  2. $$\sin x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$

  3. $$\sin x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$

  4. $$\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$$

Show answer
Correct Option: A,D
Explanation:

The general formula for the Madhava series is $$\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$$.

What is the name of the series that Madhava used to approximate the cosine function?

  1. Madhava series

  2. Taylor series

  3. Fourier series

  4. Maclaurin series

Show answer
Correct Option: A
Explanation:

The Madhava series is a series expansion for the cosine function that was discovered by Madhava of Sangamagrama.

What is the general formula for the Madhava series for the cosine function?

  1. $$\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots$$

  2. $$\cos x = 1 - \frac{x^2}{2} + \frac{x^4}{4} - \frac{x^6}{6} + \cdots$$

  3. $$\cos x = 1 - \frac{x^2}{2} + \frac{x^4}{4} - \frac{x^6}{6} + \cdots$$

  4. $$\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots$$

Show answer
Correct Option: A,D
Explanation:

The general formula for the Madhava series for the cosine function is $$\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots$$.

What is the name of the series that Madhava used to approximate the arctangent function?

  1. Madhava series

  2. Taylor series

  3. Fourier series

  4. Maclaurin series

Show answer
Correct Option: A
Explanation:

The Madhava series is a series expansion for the arctangent function that was discovered by Madhava of Sangamagrama.

What is the general formula for the Madhava series for the arctangent function?

  1. $$\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$

  2. $$\arctan x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$$

  3. $$\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$

  4. $$\arctan x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$$

Show answer
Correct Option: A,C
Explanation:

The general formula for the Madhava series for the arctangent function is $$\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$.

What is the name of the series that Madhava used to approximate the pi?

  1. Madhava series

  2. Taylor series

  3. Fourier series

  4. Maclaurin series

Show answer
Correct Option: A
Explanation:

The Madhava series is a series expansion for pi that was discovered by Madhava of Sangamagrama.

What is the general formula for the Madhava series for pi?

  1. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  2. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  3. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  4. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

Show answer
Correct Option: A,B,C,D
Explanation:

The general formula for the Madhava series for pi is $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$.

What is the name of the series that Madhava used to approximate the area of a circle?

  1. Madhava series

  2. Taylor series

  3. Fourier series

  4. Maclaurin series

Show answer
Correct Option: A
Explanation:

The Madhava series is a series expansion for the area of a circle that was discovered by Madhava of Sangamagrama.

What is the general formula for the Madhava series for the area of a circle?

  1. $$A = \pi r^2 = \frac{4r^2}{3} \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  2. $$A = \pi r^2 = \frac{4r^2}{3} \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  3. $$A = \pi r^2 = \frac{4r^2}{3} \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  4. $$A = \pi r^2 = \frac{4r^2}{3} \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

Show answer
Correct Option: A,B,C,D
Explanation:

The general formula for the Madhava series for the area of a circle is $$A = \pi r^2 = \frac{4r^2}{3} \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$.

What is the name of the series that Madhava used to approximate the volume of a sphere?

  1. Madhava series

  2. Taylor series

  3. Fourier series

  4. Maclaurin series

Show answer
Correct Option: A
Explanation:

The Madhava series is a series expansion for the volume of a sphere that was discovered by Madhava of Sangamagrama.

What is the general formula for the Madhava series for the volume of a sphere?

  1. $$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi r^3 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  2. $$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi r^3 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  3. $$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi r^3 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

  4. $$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi r^3 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$

Show answer
Correct Option: A,B,C,D
Explanation:

The general formula for the Madhava series for the volume of a sphere is $$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi r^3 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$.

What is the name of the series that Madhava used to approximate the circumference of an ellipse?

  1. Madhava series

  2. Taylor series

  3. Fourier series

  4. Maclaurin series

Show answer
Correct Option: A
Explanation:

The Madhava series is a series expansion for the circumference of an ellipse that was discovered by Madhava of Sangamagrama.

What is the general formula for the Madhava series for the circumference of an ellipse?

  1. $$C = 4aE(e) = 4a \left(1 - \frac{e^2}{2} + \frac{e^4}{2\cdot4} - \frac{e^6}{2\cdot4\cdot6} + \cdots\right)$$

  2. $$C = 4aE(e) = 4a \left(1 - \frac{e^2}{2} + \frac{e^4}{2\cdot4} - \frac{e^6}{2\cdot4\cdot6} + \cdots\right)$$

  3. $$C = 4aE(e) = 4a \left(1 - \frac{e^2}{2} + \frac{e^4}{2\cdot4} - \frac{e^6}{2\cdot4\cdot6} + \cdots\right)$$

  4. $$C = 4aE(e) = 4a \left(1 - \frac{e^2}{2} + \frac{e^4}{2\cdot4} - \frac{e^6}{2\cdot4\cdot6} + \cdots\right)$$

Show answer
Correct Option: A,B,C,D
Explanation:

The general formula for the Madhava series for the circumference of an ellipse is $$C = 4aE(e) = 4a \left(1 - \frac{e^2}{2} + \frac{e^4}{2\cdot4} - \frac{e^6}{2\cdot4\cdot6} + \cdots\right)$$.

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