MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find C using Lagrange s mean value theorem, if f(x) = ex, a = 0, b = 1. |
| A. | e<sup>e-1</sup> |
| B. | e-1 |
| C. | log (_e^{e+1} ) |
| D. | log (_e^{e-1} ) |
| Answer» E. | |
| 2. |
What is the formula for Lagrange s theorem? |
| A. | f (c) = ( frac {f(a)+f(b)}{b-a} ) |
| B. | f (c) = ( frac {f(b)-f(a)}{b-a} ) |
| C. | f (c) = ( frac {f(a)+f(b)}{b+a} ) |
| D. | f (c) = ( frac {f(a)-f(b)}{b+a} ) |
| Answer» C. f (c) = ( frac {f(a)+f(b)}{b+a} ) | |
| 3. |
Is Rolle s theorem applicable to f(x) = tan x on [ ( frac { pi }{4}, frac {5 pi }{4} ) ]? |
| A. | Yes |
| B. | No |
| Answer» C. | |
| 4. |
Rolle s theorem is a special case of _____ |
| A. | Euclid s theorem |
| B. | another form of Rolle s theorem |
| C. | Lagrange s mean value theorem |
| D. | Joule s theorem |
| Answer» D. Joule s theorem | |
| 5. |
Lagrange s mean value theorem is also called as _____ |
| A. | Euclid s theorem |
| B. | Rolle s theorem |
| C. | a special case of Rolle s theorem |
| D. | the mean value theorem |
| Answer» E. | |
| 6. |
Function f is differentiable on [a,b] to satisfy Lagrange s mean value theorem. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 7. |
What are/is the conditions to satify Lagrange s mean value theorem? |
| A. | f is continuous on [a,b] |
| B. | f is differentiable on (a,b) |
| C. | f is differentiable and continuous on (a,b) |
| D. | f is differentiable and non-continuous on (a,b) |
| Answer» D. f is differentiable and non-continuous on (a,b) | |
| 8. |
Function f is not continuous on [a,b] to satisfy Lagrange s mean value theorem. |
| A. | False |
| B. | True |
| Answer» B. True | |
| 9. |
What is the relation between f(a) and f(h) according to another form of Rolle s theorem? |
| A. | f(a) < f(a+h) |
| B. | f(a) = f(a+h) |
| C. | f(a) = f(a-h) |
| D. | f(a) > f(a+h) |
| Answer» C. f(a) = f(a-h) | |
| 10. |
Another form of Rolle s theorem for the continuous condition is _____ |
| A. | f is continuous on [a,a-h] |
| B. | f is continuous on [a,h] |
| C. | f is continuous on [a,a+h] |
| D. | f is continuous on [a,ah] |
| Answer» D. f is continuous on [a,ah] | |
| 11. |
Another form of Rolle s theorem for the differential condition is _____ |
| A. | f is differentiable on (a,ah) |
| B. | f is differentiable on (a,a-h) |
| C. | f is differentiable on (a,a/h) |
| D. | f is differentiable on (a,a+h) |
| Answer» E. | |
| 12. |
Does Rolle s theorem applicable if f(a) is not equal to f(b)? |
| A. | Yes |
| B. | No |
| C. | Under particular conditions |
| D. | May be |
| Answer» C. Under particular conditions | |
| 13. |
What is the relation between f(a) and f(b) according to Rolle s theorem? |
| A. | Equals to |
| B. | Greater than |
| C. | Less than |
| D. | Unequal |
| Answer» B. Greater than | |
| 14. |
Function f is differential on (a,b) according to Rolle s theorem. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 15. |
Function f should be _____ on [a,b] according to Rolle s theorem. |
| A. | continuous |
| B. | non-continuous |
| C. | integral |
| D. | non-existent |
| Answer» B. non-continuous | |