Download App

Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
If $f(x)=\left\{\begin{array}{l}x, \text { if } x \leq 1 \\ 7, \text { if } x>1\end{array}\right.,$ then
✓

Answer

$f(1)=1$
$\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1} x=1, $
$\lim _{x \rightarrow 1^{+}} f(x)$
$=\lim _{x \rightarrow 1} 7=7$
Since, $f(1) \neq \lim _{x \rightarrow 1^{+}} f(x) $
$\therefore f$ is discontinuous at $x=1$

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

The value of $\sin ^{-1}\left(\cos \frac{13 \pi}{5}\right)$ is
→
Let $R$ be the relation defined on $N \times N$ by the rule $(a, b)\ R\ (c, d) \Leftrightarrow a+d=b+c$, then $R$ is
→
$\int \frac{\cos 2 x}{\sin ^2 x \cdot \cos ^2 x} d x$ is equal to
→
vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are inclined at angle $\theta=120^\circ.$ if $|\vec{\text{a}}|=1,\big|\vec{\text{b}}\big|=2,$ then $\big[\big(\vec{\text{a}}+3\vec{\text{b}}\big)\times\big(3\vec{\text{a}}-\vec{\text{b}}\big)\big]^2$ is equal to:
  1. 300
  2. 325
  3. 275
  4. 225
→
If $\text{f}\text{(x)}=\sqrt{\text{x}^2-10\text{x}+25},$ then the derivative of f(x) in the intereval [0, 7] is:
  1. 1
  2. -1
  3. 0
  4. None of these.
→
$\int\limits^\pi_0\frac{1}{\text{a}+\text{b}\cos\text{x}}\text{ dx}=$
  1. $\frac{\pi}{\sqrt{\text{a}^2-\text{b}^2}}$
  2. $\frac{\pi}{\text{ab}}$
  3. $\frac{\pi}{\text{a}^2-\text{b}^2}$
  4. $({\text{a}+\text{b}})\pi$
→
Choose the correct answer from the given four options.
A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
→
The value of $\sin\big(2\big(\tan^{-1}0.75\big)\big)$ is equal to:
→
The radius of a sphere is changing at the rate of $0.1\text{cm}/\sec.$ The rate of change of its  surface area when the radius is 200cm is:
  1. $8\pi\text{ cm}^2/\sec.$
  2. $12\pi\text{ cm}^2/\sec.$
  3. $160\pi\text{ cm}^2/\sec.$
  4. $200\text{cm}^2/\sec.$
→
The vector $\vec{\text{b}}=3\hat{\text{i}}+4\hat{\text{k}}$ is to be written as the sum of a vector $\vec{\alpha}$ parallel to $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}$ and a vector $\vec{\beta}$ perpendicular to $\vec{\text{a}}.$ Then $\vec{\alpha}=$
  1. $\frac{3}{2}\big(\hat{\text{i}}+\hat{\text{j}}\big)$
  2. $\frac{2}{3}\big(\hat{\text{i}}+\hat{\text{j}}\big)$
  3. $\frac{1}{2}\big(\hat{\text{i}}+\hat{\text{j}}\big)$
  4. $\frac{1}{3}\big(\hat{\text{i}}+\hat{\text{j}}\big)$
→