MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 11 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the value of ( lim_{x rightarrow 0} frac{xsin(x-1)}{(x-1)e^x} ) is, where {x} is the fractional part of x. |
| A. | <sup>2</sup> <sub>e</sub> |
| B. | <sup>1</sup> <sub>e</sub> |
| C. | 0 |
| D. | <sup>1</sup> <sub>e</sub> |
| Answer» C. 0 | |
| 2. |
If f(x) = ex + xcos(x) and g(x) = Sin(x) than find value of limx 0 f(x) g(x) |
| A. | 2 |
| B. | 1 |
| C. | 3 |
| D. | 4 |
| Answer» B. 1 | |
| 3. |
If f(x) = sin(x)cos(x) and g(x) = x2 than find value of limx 0 f(x) g(x) |
| A. | 2 |
| B. | 0 |
| C. | -1 |
| D. | Cannot be found |
| Answer» C. -1 | |
| 4. |
If f(x) = Sin(x) and g(x) = x than find value of limx 0 f(x) g(x) |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 5. |
If f(x) = x3 + 3x2 + Sin(x) and g(x) = ex 1 than find value of ( lim_{x rightarrow 0}f(x)^{ frac{1}{g(x)}} ) |
| A. | e<sup>6e</sup> |
| B. | e<sup>(e/6)</sup> |
| C. | e<sup>6</sup> |
| D. | e<sup>(6/e)</sup> |
| Answer» D. e<sup>(6/e)</sup> | |
| 6. |
Find the value of ( lim_{x rightarrow infty}(1+ frac{1}{x})^x ) |
| A. | e-1 |
| B. | e |
| C. | e + 1 |
| D. | 1 |
| Answer» C. e + 1 | |
| 7. |
If f(x) = Tan(x) and g(x) = ex 1 than find value of limx 0 f(x) g(x) |
| A. | 1 |
| B. | 0 |
| C. | -1 |
| D. | 2 |
| Answer» B. 0 | |
| 8. |
If f(x) = Tan(x)-1 and g(x) = Sin(x) Cos(x) than find value of limx 4 f(x) g(x) |
| A. | - 2 |
| B. | (-2) |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 9. |
If f(x) = x2 3x + 2 and g(x) = x3 x2 + x 1 than find value of ( lim_{x rightarrow 1} frac{f(x)}{g(x)} )? |
| A. | 0.5 |
| B. | 1 |
| C. | -.5 |
| D. | -1 |
| Answer» D. -1 | |
| 10. |
L Hospital Rule states that |
| A. | If ( lim_{x rightarrow a} frac{f(x)}{g(x)} ) is an indeterminate form than ( lim_{x rightarrow a} frac{f(x)}{g(x)}= lim_{x rightarrow a} frac{f'(x)}{g'(x)} ) if ( lim_{x rightarrow a} frac{f'(x)}{g'(x)} ) has a finite value |
| B. | ( lim_{x rightarrow a} frac{f(x)}{g(x)} ) always equals to ( lim_{x rightarrow a} frac{f'(x)}{g'(x)} ) |
| C. | ( lim_{x rightarrow a} frac{f(x)}{g(x)} ) if an indeterminate form than cannot be solved |
| D. | ( lim_{x rightarrow a} frac{f(x)}{g(x)} ) if an indeterminate form than it is equals to zero. |
| Answer» B. ( lim_{x rightarrow a} frac{f(x)}{g(x)} ) always equals to ( lim_{x rightarrow a} frac{f'(x)}{g'(x)} ) | |
| 11. |
What are Intermediate Forms? |
| A. | Forms(f(x)/g(x)) whose limits x tends to a can give rational number directly |
| B. | Forms(f(x)/g(x)) whose limits x tends to a can give finite number directly |
| C. | Forms(f(x)/g(x)) whose limits x tends to a can not be infinite output or cannot be solved directly |
| D. | Forms(f(x)/g(x)) whose limits x tends to a can gives finite output |
| Answer» D. Forms(f(x)/g(x)) whose limits x tends to a can gives finite output | |