Question 1

For a given graph, what will be the Fourier series?

Accepted Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Answer

None of the above.

Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Question 2

Let $f(x) = e^{-x}, ext{for} ~-2 \leq x < 1,
ewline
= -2x^2, ext{for}~1 \leq x < 2,
ewline
= 4,~ ext{for}~x = 2.$ Then the Fourier series converges to

Accepted Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Answer

the sum of Cosine series only.

Answer

the sum of Cosine and Sine series along with the constant term.

Answer

the sum of Sine series only.

Question 3

What will be the differential equation of the set of all right circular cones whose axes coincide with the z-axis?

Accepted Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Answer

Can't be determined from the given information.

Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Question 4

The general solution of $f(x) = e^{-x}, ext{for} ~-2 \leq x < 1,
ewline
= -2x^2, ext{for}~1 \leq x < 2,
ewline
= 4,~ ext{for}~x = 2.$ is

Accepted Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

Answer

$-0.25 + 16/\pi^2 \sum_{n=1}^{\infty} 1/n^2 (1 - 2~ cos (n\pi/2))
ewline + cos ((3n\pi/4))* cos (n\pi x/8).$

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