Question:medium
If
\( f(x) =
\begin{cases}
1, & 0 < x \le \dfrac{3\pi}{4} \\
2\sin\left(\dfrac{2x}{9}\right), & \dfrac{3\pi}{4} < x < \pi
\end{cases}
\)
then:
If
\( f(x) = \begin{cases} 1, & 0 < x \le \dfrac{3\pi}{4} \\ 2\sin\left(\dfrac{2x}{9}\right), & \dfrac{3\pi}{4} < x < \pi \end{cases} \)
then:
\( f(x) = \begin{cases} 1, & 0 < x \le \dfrac{3\pi}{4} \\ 2\sin\left(\dfrac{2x}{9}\right), & \dfrac{3\pi}{4} < x < \pi \end{cases} \)
then:
Show Hint
Check continuity only at boundary points of piecewise functions.
Updated On: Mar 20, 2026
- \(f(x)\) is continuous at \(x=0\)
- \(f(x)\) is continuous at \(x=\pi\)
- \(f(x)\) is continuous at \(x=\frac{3\pi}{4}\)
- f(x) is discontinuous at x=(3π)/(4)
Show Solution
The Correct Option is C
Solution and Explanation
Was this answer helpful?
0
Top Questions on 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
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
Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as
(i) Find \(f'(x)\) for \(0<x>3\).
(ii) Find \(f'(4)\).
(iii)(a) Test for continuity of \(f(x)\) at \(x=3\).
OR
(iii)(b) Test for differentiability of \(f(x)\) at \(x=3\).
- CBSE Class XII - 2026
- Mathematics
- Continuity and differentiability
- Want to practice more? Try solving extra ecology questions todayView All Questions