Download App

Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
The function $f(x)=[x]$, where $[x]$ denotes the greatest integer less than or equal to $x$, is continuous at
✓

Answer

Let $x=1.5$
$\therefore$ L.H.L. $=\operatorname{Lt}_{x \rightarrow 1.5^{-}} f(x)=\underset{h \rightarrow 0}{\operatorname{Lt}}[1.5-h]=1$
and R.H.L. $=\operatorname{Lt}_{x \rightarrow 1.5^{+}} f(x)=\underset{h \rightarrow 0}{\operatorname{Lt}}[1.5+h]=1$
$\because \quad$ L.H.L. = R.H.L.
$\therefore f(x)$ is continuous at $x=1.5$
Also, greatest integer function is discontinuous at all integral values of $x$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Continuity and Differentiability→Continuity and Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to:
  1. $\frac{2}{\pi}\ \text{unit}$
  2. $\frac{1}{\pi}\ \text{unit}$
  3. $\frac{\pi}{2}\ \text{unit}$
  4. $\pi \ \text{unit}$
→
If $\text{A}=\begin{bmatrix} 1 2 -1 -1\  1\  2\  2 -1\ 1 \end{bmatrix},$ then det $($adj $($adj $A))$ is:
→
The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If the maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0), then:
→
The differential equation of all parabolas whose axes are parallel to y-axis is:
  1. $\frac{\text{dy}}{\text{dx}}=-\frac{\text{c}^2}{\text{x}^2}$
  2. $\frac{\text{d}^2\text{x}}{\text{dy}^2}=\text{c}$
  3. $\frac{\text{d}^3\text{y}}{\text{dx}^3}+\frac{\text{d}^2\text{x}}{\text{dy}^2}=0$
  4. $\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\frac{\text{dy}}{\text{dx}}=0$
→
If $f(x)=\sqrt{1+\cos ^2\left(x^2\right)}$, then the value of $f^{\prime}\left(\frac{\sqrt{\pi}}{2}\right)$ is
→
The angle between the two diagonals of a cube is:
→
Write the number of points where f(x) = |x + 2| + |x - 3| is not differentiable:
  1. 2
  2. 0
  3. 1
  4. 3
→
A solution of the differential equation $\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}+y=0$ is
→
Refer to Question 18 (Maximum value of Z+ Minimum value of Z) is equal to:
→
Evaluate: $\int \frac{d x}{\sqrt{1-2 x-x^2}}$
→