MCQOPTIONS
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MCQOPTIONS
This section includes 10 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 the sum of ( frac{1}{1^2} + frac{1}{3^2} + frac{1}{5^2} ) + using Fourier series expansion if f(x) = a when [0, ] and 2 x when [ , 2 ]. |
| A. | ( frac{ ^2}{8} ) |
| B. | ( frac{ ^2}{4} ) |
| C. | ( frac{ ^2}{16} ) |
| D. | ( frac{ ^2}{2} ) |
| Answer» B. ( frac{ ^2}{4} ) | |
| 4. |
Find a0 of the function (f(x) = frac{1}{4} ( -x)^2. ) |
| A. | ( frac{ ^2}{6} ) |
| B. | ( frac{ ^2}{12} ) |
| C. | (5 frac{ ^2}{6} ) |
| D. | (5 frac{ ^2}{12} ) |
| Answer» B. ( frac{ ^2}{12} ) | |
| 5. |
Find a0 of the function (f(x) = sqrt{ frac{1-cosx}{2}}. ) |
| A. | ( frac{4}{ } ) |
| B. | ( frac{2}{ } ) |
| C. | ( frac{ }{4} ) |
| D. | ( frac{ }{2} ) |
| Answer» B. ( frac{2}{ } ) | |
| 6. |
If the function f(x) is odd, then which of the only coefficient is present? |
| A. | a<sub>n</sub> |
| B. | b<sub>n</sub> |
| C. | a<sub>0</sub> |
| D. | everything is present |
| Answer» C. a<sub>0</sub> | |
| 7. |
If the function f(x) is even, then which of the following is zero? |
| A. | a<sub>n</sub> |
| B. | b<sub>n</sub> |
| C. | a<sub>0</sub> |
| D. | nothing is zero |
| Answer» C. a<sub>0</sub> | |
| 8. |
What is the Fourier series expansion of the function f(x) in the interval (c, c+2 )? |
| 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) ) | |
| 9. |
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)] ) | |
| 10. |
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. | |