MCQOPTIONS
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MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Differential Calculus knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Maclaurin s Theorem is a special type of Taylor s Theorem. |
| A. | False |
| B. | True |
| Answer» C. | |
| 2. |
Maclaurin Series is named after ______________ |
| A. | Colin Maclaurin |
| B. | Normand Maclaurin |
| C. | Ian Maclaurin |
| D. | Richard Cockburn Maclaurin |
| Answer» B. Normand Maclaurin | |
| 3. |
For the power series of the form, ( _{i=0}^ a_i z^i, ) which one of the following may not be true? |
| A. | The series converges only for z=0 |
| B. | The series converges absolutely for all z |
| C. | The series converges absolutely for all z in some finite open interval (-R, R) and diverges if z<-R or z>R |
| D. | At the points z=R and z=-R, the series will diverge |
| Answer» E. | |
| 4. |
The initial condition for the recurrence relation of a factorial is ___________ |
| A. | 0!=0 |
| B. | 0!=1 |
| C. | 1!=1 |
| D. | 1!=0 |
| Answer» C. 1!=1 | |
| 5. |
What is the first term in the Taylor series expansion of f(x) = 8x5-3x2-5x about x=2? |
| A. | 232 |
| B. | 244 |
| C. | 234 |
| D. | 222 |
| Answer» D. 222 | |
| 6. |
What is the Taylor series expansion of f(x)= x2-x+1 about the point x=-1? |
| A. | f(x) = -3-3(x+1)+(x+1)<sup>2</sup> |
| B. | f(x) = -3-(x+1)+(x+1)<sup>2</sup> |
| C. | f(x) = -3-3(x+1)+2(x+1)<sup>2</sup> |
| D. | f(x) = -1-3(x+1)+2(x+1)<sup>2</sup> |
| Answer» B. f(x) = -3-(x+1)+(x+1)<sup>2</sup> | |
| 7. |
Cauchy s Remainder for Maclaurin s Theorem is given by ( frac{x^n(1- )^{n-1}}{(n-1)!}f^{(n)}( x) ). |
| A. | True |
| B. | False |
| Answer» B. False | |
| 8. |
Lagrange s Remainder for Maclaurin s Theorem is given by _____________ |
| A. | ( frac{x^n}{(n-1)!}f^{(n)}( x) ) |
| B. | ( frac{x^n}{n!} f^{(n)}( x) ) |
| C. | ( frac{x^{n-1}}{n!} f^{(n)}( x) ) |
| D. | ( frac{x^n}{n!}f^{(n-1)}( x) ) |
| Answer» C. ( frac{x^{n-1}}{n!} f^{(n)}( x) ) | |
| 9. |
Taylor s theorem was stated by the mathematician _____________ |
| A. | Brook Taylor |
| B. | Eva Germaine Rimington Taylor |
| C. | Sir Geoffrey Ingram Taylor |
| D. | Michael Eugene Taylor |
| Answer» B. Eva Germaine Rimington Taylor | |