Question:
The value of C in Rolle's theorem where \(-\frac{π}{2}\)<C<\(\frac{π}{2}\) and \(f(x)=cos x\) on \([-\frac{π}{2},\frac{π}{2}]\) is equal to :
The value of C in Rolle's theorem where \(-\frac{π}{2}\)<C<\(\frac{π}{2}\) and \(f(x)=cos x\) on \([-\frac{π}{2},\frac{π}{2}]\) is equal to :
Updated On: Mar 12, 2025
- 0
- π
- \(\frac{π}{2}\)
- \(\frac{π}{4}\)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is(A):0
Was this answer helpful?
0
0
Top Questions on Continuity and differentiability
Let $\alpha,\beta\in\mathbb{R}$ be such that the function \[ f(x)= \begin{cases} 2\alpha(x^2-2)+2\beta x, & x<1 \\ (\alpha+3)x+(\alpha-\beta), & x\ge1 \end{cases} \] is differentiable at all $x\in\mathbb{R}$. Then $34(\alpha+\beta)$ is equal to}
- JEE Main - 2026
- Mathematics
- Continuity and differentiability
- If \[ f(x) = \begin{cases} \dfrac{a|x| + x^2 - 2(\sin|x|)(\cos|x|)}{x}, & x \ne 0, \\ b, & x = 0, \end{cases} \] is continuous at \( x = 0 \), then \( a + b \) is equal to.
- JEE Main - 2026
- Mathematics
- Continuity and differentiability
- Let \[ f(x)=\lim_{\theta\to 0}\frac{\cos(\pi x)-x^{2/\theta}\sin(x-1)}{1-x^{2/\theta}(x-1)}. \] Statement 1: \(f(x)\) is discontinuous at \(x=1\).
Statement 2: \(f(x)\) is continuous at \(x=-1\).- JEE Main - 2026
- Mathematics
- Continuity and differentiability
- (a) Differentiate $\sqrt{e^{\sqrt{2x}}}$ with respect to $e^{\sqrt{2x}}$ for $x>0$.
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
View More Questions
Questions Asked in CUET PG exam
- Upper palaeolithic culture in India is dominated by:
- CUET (PG) - 2025
- Prehistoric Archaeology
- Which of the following species are included among gracile australopithecines?
A. A. africanus
B. A. boisei
C. A. afarensis
D. A. anamensis
Choose the correct answer from the options given below:- CUET (PG) - 2025
- Paleoanthropology
- A bought an article at a certain price and sold it at 10% profit. B bought the same article at a price 10% lesser than A and sold it at ₹18 lesser than A. B's gain percentage in this deal is 20%. At what price B bought the article?
- CUET (PG) - 2025
- Profit and Loss
- The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8:20:00 hours, then at what time will they again change simultaneously?
- CUET (PG) - 2025
- Quantitative Aptitude
- In terracotta which materials are mainly used to build strong clay
(A) Grog
(B) Metal
(C) Cotton
(D) Stone
Choose the correct answer from the options given below:- CUET (PG) - 2025
- Ceramics and Pottery
View More Questions