$A$ function $f$ from $R$ to $R$ is continuous at a point $a \in R$ if for each $\epsilon > 0$,there exists $\delta > 0$ such that:
- A$|f(x) - f(a)| < \epsilon \implies |x - a| < \delta$
- B$|f(x) - f(a)| > \epsilon \implies |x - a| > \delta$
- C$|x - a| > \delta \implies |f(x) - f(a)| > \epsilon$
- D$|x - a| < \delta \implies |f(x) - f(a)| < \epsilon$
Explore More
Similar Questions
Let $f(x)$ be a real-valued function. If $f^{\prime}(x)$ is a constant for all $x \in R$,$f(0)=2$,and $f^{\prime}(0)=1$,then
If the real valued function $f(x) = \begin{cases} \frac{\cos 3x - \cos x}{x \sin x} & \text{if } x < 0 \\ p & \text{if } x = 0 \\ \frac{\log(1 + q \sin x)}{x} & \text{if } x > 0 \end{cases}$ is continuous at $x = 0$, then $p + q =$
Let $f(x) = \begin{cases} x^2 + k, & \text{when } x \ge 0 \\ -x^2 - k, & \text{when } x < 0 \end{cases}$. If the function $f(x)$ is continuous at $x = 0$,then $k =$
Easy
View SolutionIf $f(x) = \int_{-1}^x |t| \, dt$,$x \ge -1$,then
Difficult
View SolutionIf $f(x) = \frac{\log_{\sin |x|} \cos^3 x}{\log_{\sin |3x|} \cos^3 (x/2)}$ for $|x| < \frac{\pi}{3}, x \neq 0$ and $f(0) = 4$,then the number of points of discontinuity of $f$ in $\left( -\frac{\pi}{3}, \frac{\pi}{3} \right)$ is:
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo