Download App

Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
For which value of $k$, this funciton is continuous at $x=1$.$
f(x)=\left\{\begin{array}{cc}
\frac{x^2-3 x+2}{x-1}, & x \neq 1 \\
k, & x=1
\end{array}\right.
$
✓

Answer

$(B)$
value of function at $x=1$
$f(1)=k$
Value of $\text{R.H.L.}$
$\lim _{h \rightarrow 0} f(1+h)=\lim _{h \rightarrow 0} \frac{(1+h)^2-3(1+h)+2}{1+h-1}$
$=\lim _{h \rightarrow 0} \frac{1+2 h+h^2-3-3 h+2}{h}$
$=\lim _{h \rightarrow 0} \frac{h^2-h}{h}=\lim _{h \rightarrow 0}[h-1]=-1$
because function is continuous at $x=1$, so
$f(1)=\text{ R . H . L .}$
$\therefore k=-1$
Hence correct option is $(B).$

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

Let $A=\{1,2,3\}$ and consider the relation $R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$. Then $R$ is
→
What is the value of $ \cos^{-1}(-\text{x})$ for all x belongs to [-1, 1]?
  1. $ \cos^{-1}(-\text{x})$
  2. $\pi- \cos^{-1}(-\text{x})$
  3. $ π – \cos-1(-\text{x})$
  4. $ π – \cos-1(+\text{x})$
→
Let f : R → R be a function defined by $\text{f(x)}=\frac{\text{e}^{|\text{x}|}-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}.$ Then,
  1. f is a bijection.
  2. f is an injection only.
  3. f is surjection on only.
  4. f is neither an injection nor a surjection.
→
Choose the correct answers from the given four options:
If $\text{y}=\log\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big),$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:
  1. $\frac{4\text{x}^3}{1-\text{x}^4}$
  2. $\frac{-4\text{x}}{1-\text{x}^4}$
  3. $\frac{1}{4-\text{x}^4}$
  4. $\frac{-4\text{x}^3}{1-\text{x}^4}$
→
A coin is tossed three times. If events A and B are defined as A = Two heads come, B = Last should be head, Then, A and B are
  1. Independent.
  2. Dependent.
  3. Both.
  4. Mutually exclusive.
→
Find the principal values of: $\tan ^{-1}(\sqrt{3})$
→
If $A$ is a matrix of order $3$ and $|A| = 8$, then $|\text{adj} A| =$
→
If $\tan ^{-1}\left(\frac{3}{4}\right)=\theta$ then value of $\sin \theta$ is :
→
One hundred idential coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is:
→
Integrating factor of the differential equation $\left(1-x^2\right) \frac{d y}{d x}-x y=1$ is
→