Download App

Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
The function $\text{f{x}}\begin{cases}1,&|\text{x}|\geq1\\\frac{1}{\text{n}^2},&\frac{1}{\text{n}} < |\text{x}| < \frac{1}{\text{n}-1},\text{n}=2,3,...\end{cases}$
  • A
    Is discontinuous at finitely many points.
  • B
    Is continuous everywher.
  • ✓
    Is discontinuous only at $\text{x}=\pm\frac{1}{\text{n}},\text{n }\in\text{ z}-\{0\}$ and $x = 0$
  • D
    None of these.
✓

Answer

Correct option: C.
Is discontinuous only at $\text{x}=\pm\frac{1}{\text{n}},\text{n }\in\text{ z}-\{0\}$ and $x = 0$
Given function is
$\text{f{x}}\begin{cases}1,&|\text{x}|\geq1\\\frac{1}{\text{n}^2},&\frac{1}{\text{n}} < |\text{x}| < \frac{1}{\text{n}-1},\text{n}=2,3,...\end{cases}$
Consider,
$\lim\limits_{\text{x}\rightarrow\frac{1}{\text{n}}^-}\text{f(x)}=\frac{1}{\text{n}^2}$
$\lim\limits_{\text{x}\rightarrow\frac{1}{\text{n}}^+}\text{f(x)}=\lim\limits_{\text{x}\rightarrow\frac{1}{\text{n}}}1=1$
Hence, fnuction is discontinuous at $\text{x}=\pm\frac{1}{\text{n}},\text{n }\in\text{ z}-\{0\}$ and $x = 0$

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\overrightarrow{ u }, \overrightarrow{ v }$ and $\overrightarrow{ w }$ be vectors in three-dimensional space, where $\overrightarrow{ u }$ and $\overrightarrow{ v }$ are unit vectors which are not perpendicular to each other and $\overrightarrow{ u } \cdot \overrightarrow{ w }=1, \overrightarrow{ v } \cdot \overrightarrow{ w }=1, \overrightarrow{ w } \cdot \overrightarrow{ w }=4$

If the volume of the parallelopiped, whose adjacent sides are represented by the vectors $\overrightarrow{ u }, \overrightarrow{ v }$ and $\overrightarrow{ w }$ , is $\sqrt{2}$, then the value of $|3 \vec{u}+5 \vec{v}|$ is. . . . .

→
If $A = [a_{ij}]$ is a square matrix of even order such that $a_{ij} = i^2 - j^2,$ then
→
Find the projection of the vector $\hat{i}+3 \hat{j}+7 \hat{k}$ on the vector $2 \hat{i}-3 \hat{j}+6 \hat{k}$.
→
If $\displaystyle \text{a}_{\text{ij}}=0\left (\text{i}\neq \text{j} \right )$ and $\displaystyle\text{a}_{\text{ij}}=2\left (\text{i= j} \right )$ then the matrix $\text{A}=\displaystyle \left [ \text{a}_{\text{ij}} \right ]_{\text{n}\times\text{n}}$ ​ is a _______ matrix ?
→
If the rate of chage of volume of sphere is equal to the rate of change of its radius, then its radius is equal to :
→
Vikas printing company takes fee of Rs. 28 to print a oversized poster and Rs. 7 for each colour of ink used. Raaj printing company does the same work and charges poster for Rs. 34 and Rs. 5.50 for each colour of ink used. If z is the colours of ink used, find the values of z such that Vikas printing company would charge more to print a poster than Raaj printing company.
→
If $\theta_{1}$ and $\theta_{2}$ be respectively the smallest and the largest values of $\theta$ in $(0,2 \pi)-\{\pi\}$ which satisfy the equation, $\quad 2 \cot ^{2} \theta-\frac{5}{\sin \theta}+4=0,$ then $\int\limits_{\theta_{1}}^{\theta_{2}} \cos ^{2} 3 \theta \mathrm{d} \theta $ is equal to
→
The area bounded by the curve $x^2=4 y+4$ and line $3 x+4 y=0$ is:
→
If $A$ and $B$ are two non-zero $n \times n$ matrics such that $A ^2+ B = A ^2 B$, then
→
For any three vectors $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ the expression $\big(\vec{\text{a}}-\vec{\text{b}}\big).\big\{\big(\vec{\text{b}}-\vec{\text{c}}\big)\times\big(\vec{\text{c}}-\vec{\text{a}}\big)\big\}$ equals:
→