MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Determine the radius of convergence and interval of convergence for the power series: ∞∑n=0 (x−7)n+1/nn. |
| A. | 0, −1<x<1 |
| B. | ∞, −∞<x<∞ |
| C. | 1, −2<x<2 |
| D. | 2, −1<x<1 |
| Answer» C. 1, −2<x<2 | |
| 2. |
What is the radius of convergence and interval of convergence for the power series ∞∑n=0m!(2x-1)m? |
| A. | 3, 12 |
| B. | 1, 0.87 |
| C. | 2, 5.4 |
| D. | 0, 1/2 |
| Answer» E. | |
| 3. |
Find the power series representation for the function f(x)=x/4−x. |
| A. | ∞∑n=0xn+1/4n+1 |
| B. | ∞∑n=0xn+14n |
| C. | ∞∑n=0xn4n |
| D. | ∞∑n=0xn+1 |
| Answer» B. ∞∑n=0xn+14n | |
| 4. |
An example of Maclaurin series is _______ |
| A. | ∞∑n=0 (xn/n!) |
| B. | ∞∑n=0 (x/5+n!) |
| C. | ∞∑n=0 (xn+1/(n-1)!) |
| D. | (xn/n) |
| Answer» B. ∞∑n=0 (x/5+n!) | |
| 5. |
Determine a power series representation for the function g(x)=ln(7−x). |
| A. | ∞∑n=0 xn+1/7n+1 |
| B. | ln(14)∞∑n=0 xn+1/7n |
| C. | ln(7)∞∑n=0 xn+1/7n+1 |
| D. | ln∞∑n=0 x/7n+1 |
| Answer» D. ln∞∑n=0 x/7n+1 | |
| 6. |
Determine the interval and radius of convergence for the power series: ∞∑n=17n/n(3x−1)n-1. |
| A. | (2x+1)/6 |
| B. | 7|3x−1| |
| C. | 5|x+1| |
| D. | 3!*|4x−9| |
| Answer» C. 5|x+1| | |
| 7. |
sec(x) has a trigonometric series that is given by _______ |
| A. | ∞∑n=0 ((-1)nE2n / (2n)!)*x2n |
| B. | ∞∑n=0 ((-1)nE2n) |
| C. | ((-1)nB2n / (2n)!)*x2n |
| D. | ∞∑n=0 ((2n)!)*x2n+1 |
| Answer» B. ∞∑n=0 ((-1)nE2n) | |
| 8. |
Which of the following series is called the “formal power series”? |
| A. | b0+b1x+b2x2+…+bnxn |
| B. | b1x+b2x2+…+bnxn |
| C. | 1/2b0+1/3b1x+1/4b2x2+…+1/nbnxn |
| D. | n2(b0+b1x+b2x2+…+bnxn) |
| Answer» B. b1x+b2x2+…+bnxn | |
| 9. |
The third term of a geometric progression with common ratio equal to half the initial term is 81. Determine the 12th term. |
| A. | 312 |
| B. | 415 |
| C. | 68 |
| D. | 59 |
| Answer» B. 415 | |
| 10. |
The explicit formula for the geometric sequence 3, 15, 75, 375,… is _______ |
| A. | 2*6! * 3n-1 |
| B. | 3 * 5n-1 |
| C. | 3! * 8n-1 |
| D. | 7 * 4n-1 |
| Answer» C. 3! * 8n-1 | |