If f(x) = [a+13 sinx] & x ε (0, \(\pi\)), then number of non-differentiable points of f(x) are [where 'a' is integer]
If f(x) = [a+13 sinx] & x ε (0, \(\pi\)), then number of non-differentiable points of f(x) are [where 'a' is integer]
Correct Answer: 25
Solution and Explanation
⇒ 24 points
and also where the sin x = 1 ⇒ 1 points.
Therefore, 25 points of non-derivability
Top Questions on Continuity and differentiability
- If \[ f(x) = \begin{cases} \frac{\log(1 + ax) + \log(1 - bx)}{x}, & \text{for } x \neq 0 \\ k, & \text{for } x = 0 \end{cases} \] is continuous at $x = 0$, then the value of $k$ is:
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- If $\tan^{-1} (x^2 - y^2) = a$, where $a$ is a constant, then $\frac{dy}{dx}$ is:
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- Let \( y=\sin(\cos(x^2)) \). Find \( \frac{dy}{dx} \) at \( x=\frac{\sqrt{\pi}}{2} \).
- CUET (UG) - 2025
- Mathematics
- Continuity and differentiability
- If the function f(x) = $\begin{cases}\frac{k\cos x}{\pi - 2x} & ; x \neq \frac{\pi}{2} \\ 3 & ; x = \frac{\pi}{2} \end{cases}$ is continuous at x = $\frac{\pi}{2}$, then k is equal to
- CUET (UG) - 2025
- Mathematics
- Continuity and differentiability
Match List-I with List-II
List-I List-II (A) \( f(x) = |x| \) (I) Not differentiable at \( x = -2 \) only (B) \( f(x) = |x + 2| \) (II) Not differentiable at \( x = 0 \) only (C) \( f(x) = |x^2 - 4| \) (III) Not differentiable at \( x = 2 \) only (D) \( f(x) = |x - 2| \) (IV) Not differentiable at \( x = 2, -2 \) only
Choose the correct answer from the options given below:- CUET (UG) - 2025
- Mathematics
- Continuity and differentiability
Questions Asked in JEE Main exam
- Let circle $C$ be the image of
$$ x^2 + y^2 - 2x + 4y - 4 = 0 $$
in the line
$$ 2x - 3y + 5 = 0 $$
and $A$ be the point on $C$ such that $OA$ is parallel to the x-axis and $A$ lies on the right-hand side of the centre $O$ of $C$.
If $B(\alpha, \beta)$, with $\beta < 4$, lies on $C$ such that the length of the arc $AB$ is $\frac{1}{6}$ of the perimeter of $C$, then $\beta - \sqrt{3}\alpha$ is equal to: - Assume a living cell with 0.9%(\(w/w\)) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data up to first decimal place only) The cell will:
- JEE Main - 2025
- osmosis
Given below are two statements:
Statement (I):
are isomeric compounds.
Statement (II):
are functional group isomers.
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Isomerism
- Let \( [x] \) denote the greatest integer function, and let \( m \) and \( n \) respectively be the numbers of the points, where the function \( f(x) = [x] + |x - 2| \), \( -2<x<3 \), is not continuous and not differentiable. Then \( m + n \) is equal to:
- JEE Main - 2025
- Differential Equations
The effect of temperature on the spontaneity of reactions are represented as: Which of the following is correct?
- JEE Main - 2025
- Thermodynamics and Work Done
Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.