MCQOPTIONS
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MCQOPTIONS
This section includes 10 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. |
L’Hospital’s Rule was first discovered by Marquis de L’Hospital. |
| A. | True |
| B. | False |
| Answer» C. | |
| 2. |
What is the value of the given limit, \(\lim_{x\to 0}\frac{2}{x}\)? |
| A. | 2 |
| B. | 0 |
| C. | 1/2 |
| D. | 3/2 |
| Answer» B. 0 | |
| 3. |
Which of the following method is used to simplify the evaluation of limits? |
| A. | Cauchy’s Mean Value Theorem |
| B. | Rolle’s Theorem |
| C. | L’Hospital Rule |
| D. | Fourier Transform |
| Answer» D. Fourier Transform | |
| 4. |
What is the value of c which lies in [1, 2] for the function f(x)=4x and g(x)=3x2? |
| A. | 1.6 |
| B. | 1.5 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 5. |
What is the largest possible value of f(0), where f(x) is continuous and differentiable on the interval [-5, 0], such that f(-5)= 8 and f'(c)≤2. |
| A. | 2 |
| B. | -2 |
| C. | ≤2.a) 2b) -2c) 18 |
| D. | -18 |
| Answer» C. ≤2.a) 2b) -2c) 18 | |
| 6. |
Find the value of c which satisfies the Mean Value Theorem for the given function,f(x)= x2+2x+1 on [1,2]. |
| A. | \(\frac{-7}{2} \) |
| B. | \(\frac{7}{2} \) |
| C. | \(\frac{13}{2} \) |
| D. | \(\frac{-13}{2} \) |
| Answer» B. \(\frac{7}{2} \) | |
| 7. |
The Mean Value Theorem was stated and proved by _______ |
| A. | Parameshvara |
| B. | Govindasvami |
| C. | Michel Rolle |
| D. | Augustin Louis Cauchy |
| Answer» E. | |
| 8. |
Cauchy’s Mean Value Theorem is also known as ‘Extended Mean Value Theorem’. |
| A. | False |
| B. | True |
| Answer» C. | |
| 9. |
Which of the following is not a necessary condition for Cauchy’s Mean Value Theorem?a) The functions, f(x) and g(x) be continuous in [a, b] b) The derivation of g'(x) be equal to 0c) The functions f(x) and g(x) be derivable in (a, b)d) There exists a value c Є (a, b) such that, \(\frac{f(b)-f(a)}{g(b)-g( |
| A. | The functions, f(x) and g(x) be continuous in [a, b] b) The derivation of g'(x) be equal to 0c) The functions f(x) and g(x) be derivable in (a, b)d) There exists a value c Є (a, b) such that, \(\frac{f(b)-f(a)}{g( |
| B. | The derivation of g'(x) be equal to 0c) The functions f(x) and g(x) be derivable in (a, b)d) There exists a value c Є (a, b) such that, \(\frac{f(b)-f(a)}{g(b)-g(a)} = \frac{f'(c)}{g'( |
| C. | The functions f(x) and g(x) be derivable in (a, b) |
| D. | There exists a value c Є (a, b) such that, \(\frac{f(b)-f(a)}{g(b)-g(a)} = \frac{f'(c)}{g'(c)}\) |
| Answer» C. The functions f(x) and g(x) be derivable in (a, b) | |
| 10. |
Cauchy’s Mean Value Theorem can be reduced to Lagrange’s Mean Value Theorem. |
| A. | True |
| B. | False |
| Answer» B. False | |