Download App

Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
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.
$
  • A
    1
  • ✓
    -1
  • C
    $0$
  • D
    3
✓

Answer

Correct option: B.
-1
(B)
value of function at $x=1$
f(1)=k
Value of R.H.L.
$\lim _{h \rightarrow 0} f(1+h)=\lim _{h \rightarrow 0} \frac{(1+h)^2-3(1+h)+2}{1+h-1}$
$\begin{array}{l}=\lim _{h \rightarrow 0} \frac{1+2 h+h^2-3-3 h+2}{h} \\ =\lim _{h \rightarrow 0} \frac{h^2-h}{h}=\lim _{h \rightarrow 0}[h-1]=-1\end{array}$
because function is continuous at $x=1$, so
$\begin{array}{l}f(1)= R . H . L . \\ \therefore k=-1\end{array}$
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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $f(x) = \left\{ \begin{array}{l}1 + x,\;{\rm{when\,\, }}x \le 2\\5 - x,\,{\rm{when \,\,}}\,x \le 3\end{array} \right.$, then
→
Let $f$ be function such that $f(x + y) = f(x) + f(y)$ for all $x$ and $y$ and $f(x) = (2x^2 + 3x)g(x)$ for all $x$; where $g(x)$ is continuous and $g(0) = 3.$ Then $f '(x)$ is equal to :-
→
If the system of linear equations  $2 x + y - z =7$ ; $x-3 y+2 z=1$  ; $x +4 y +\delta z = k$, where $\delta, k \in R$  has infinitely many solutions, then $\delta+ k$ is equal to
→
In which of the following intervals is $y=x^2 e^{-x}$ increasing ?
→
Let $\quad \vec{a}=\hat{i}+\hat{j}+\hat{k}, \quad \vec{b}=-\hat{i}-8 \hat{j}+2 \hat{k} \quad$ and $\overrightarrow{\mathrm{c}}=4 \hat{\mathrm{i}}+\mathrm{c}_2 \hat{\mathrm{j}}+\mathrm{c}_3 \hat{\mathrm{k}}$ be three vectors such that $\vec{b} \times \vec{a}=\vec{c} \times \vec{a}$. If the angle between the vector $\vec{c}$ and the vector $3 \hat{i}+4 \hat{j}+\hat{k}$ is $\theta$, then the greatest integer less than or equal to $\tan ^2 \theta$ is :
→
The linear inequalities or equations or restrictions on the variables of a linear programming problem are called:
→
Choose the correct answer in each of the following:
The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is
→
The direction cosines of a line segment $AB$ are $ - 2/\sqrt {17} ,$ $3/\sqrt {17} ,\,\, - 2/\sqrt {17} .$ If $AB = \sqrt {17} $ and the co-ordinates of $A$ are $(3, -6, 10)$, then the co-ordinates of $B$ are
→
$2{\tan ^{ - 1}}(\cos x) = {\tan ^{ - 1}}({\rm{cose}}{{\rm{c}}^2}x),$ then $ x  =$
→
If g(x) = x2 + x - 2 and $\frac{1}{2}\text{gof(x)}=2\text{x}^2-5\text{x}+2,$ then f(x) is equal to:
  1. 2x - 3
  2. 2x + 3
  3. 2x2 + 3x + 1
  4. 2x2 - 3x - 1
→