MCQOPTIONS
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MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Fourier Analysis knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find bn if the function f(x) = x2. |
| A. | finite value |
| B. | infinite value |
| C. | zero |
| D. | can’t be found |
| Answer» D. can’t be found | |
| 2. |
Find an if the function f(x) = x – x3. |
| A. | finite value |
| B. | infinite value |
| C. | zero |
| D. | can’t be found |
| Answer» D. can’t be found | |
| 3. |
Find a0 of the function \(f(x) = \frac{1}{4} (π-x)^2.\) |
| A. | \(\frac{π^2}{6} \) |
| B. | \(\frac{π^2}{12} \) |
| C. | \(5\frac{π^2}{6} \) |
| D. | \(5\frac{π^2}{12} \) |
| Answer» B. \(\frac{π^2}{12} \) | |
| 4. |
Find a0 of the function \(f(x) = \sqrt{\frac{1-cosx}{2}}.\) |
| A. | \(\frac{4}{π} \) |
| B. | \(\frac{2}{π} \) |
| C. | \(\frac{π}{4} \) |
| D. | \(\frac{π}{2} \) |
| Answer» B. \(\frac{2}{π} \) | |
| 5. |
If the function f(x) is odd, then which of the only coefficient is present? |
| A. | an |
| B. | bn |
| C. | a0 |
| D. | everything is present |
| Answer» C. a0 | |
| 6. |
If the function f(x) is even, then which of the following is zero? |
| A. | an |
| B. | bn |
| C. | a0 |
| D. | nothing is zero |
| Answer» C. a0 | |
| 7. |
What is the Fourier series expansion of the function f(x) in the interval (c, c+2π)? |
| A. | \(\frac{a_0}{2}+∑_{n=1}^∞ a_n cos(nx) +∑_{n=1}^∞ b_n sin(nx) \) |
| B. | \(a_0+∑_{n=1}^∞ a_n cos(nx) +∑_{n=1}^∞ b_n sin(nx) \) |
| C. | \(\frac{a_0}{2}+∑_{n=0}^∞ a_n cos(nx) +∑_{n=0}^∞ b_n sin(nx) \) |
| D. | \(a_0+∑_{n=0}^∞ a_n cos(nx) + ∑_{n=0}^∞ b_n sin(nx) \) |
| Answer» B. \(a_0+∑_{n=1}^∞ a_n cos(nx) +∑_{n=1}^∞ b_n sin(nx) \) | |
| 8. |
At the point of discontinuity, sum of the series is equal to ___________ |
| A. | \(\frac{1}{2} [f(x+0) – f(x-0)] \) |
| B. | \(\frac{1}{2} [f(x+0) + f(x-0)] \) |
| C. | \(\frac{1}{4} [f(x+0) – f(x-0)] \) |
| D. | \(\frac{1}{4} [f(x+0) + f(x-0)] \) |
| Answer» C. \(\frac{1}{4} [f(x+0) – f(x-0)] \) | |
| 9. |
Which of the following is not Dirichlet’s condition for the Fourier series expansion? |
| A. | f(x) is periodic, single valued, finite |
| B. | f(x) has finite number of discontinuities in only one period |
| C. | f(x) has finite number of maxima and minima |
| D. | f(x) is a periodic, single valued, finite |
| Answer» E. | |