Download App

CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY1 Mark
Question
The function $\text{f(x)}=\begin{cases}\frac{\sin3\text{x}}{\text{x}},&\text{x}\ne0\\\frac{\text{k}}{2},&\text{x}=0\end{cases}$ is continuous at x = 0, then k =
  1. 3
  2. 6
  3. 9
  4. 12
✓

Answer

  1. 6

Solution:

Given, $\text{f(x)}=\begin{cases}\frac{\sin3\text{x}}{\text{x}},&\text{x}\ne0\\\frac{\text{k}}{2},&\text{x}=0\end{cases}$

If f(x) is continuous at x = 0, then

$\lim\limits_{\text{x}\rightarrow0}\text{f(x)}=\text{f}(0)$

$\Rightarrow\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{\text{x}}=\text{f}(0)$

$\Rightarrow3\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{3\text{x}}=\frac{\text{k}}{2}$

$\Rightarrow3\times1=\frac{\text{k}}{2}$

$\Rightarrow\frac{\text{k}}{2}=3$

$\Rightarrow\text{k}=6$

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 $a, b $ and $ c$ are non zero numbers, then $\Delta = \left| {\,\begin{array}{*{20}{c}}{{b^2}{c^2}}&{bc}&{b + c}\\{{c^2}{a^2}}&{ca}&{c + a}\\{{a^2}{b^2}}&{ab}&{a + b}\end{array}\,} \right|$ is equal to
→
The value of $\int_{\,0}^{\,8} {\,|x - 5|\,dx} $ is
→
A value of $c$ for which the conclusion of mean value the theorem holds for the function $f(x) = log{_e}x$ on the interval $[1, 3]$ is
→
If $\phi (x) = {x^2} + 1$ and $\psi (x) = {3^x}$, then $\phi \{ \psi (x)\} $ and $\psi \{ \phi (x)\} = $
→
Let $\overrightarrow{ a }=\hat{ i }+2 \hat{ j }-3 \hat{ k }$ and $\overrightarrow{ b }=2 \hat{ i }-3 \hat{ j }+5 \hat{ k }$. If $\overrightarrow{ r } \times \overrightarrow{ a }=\overrightarrow{ b } \times \overrightarrow{ r }, \overrightarrow{ r } \cdot(\alpha \hat{ i }+2 \hat{ j }+\hat{ k })=3$ and $\vec{r} (2 \hat{ i }+5 \hat{ j }-\alpha \hat{ k })=-1, \alpha \in R ,$ then the value of $\alpha+|\overrightarrow{ r }|^{2}$ is equal to :
→
The direction coisines of the y-axis are:
→
Suppose $X =\left[x_{i j}\right]$ a matrix, where
$
X=\left[\begin{array}{ccc}
1 & -1 & 2 \\
3 & 4 & -5 \\
2 & -1 & 3
\end{array}\right]
$
Then matrix $Y =\left[m_{i j}\right]$, where $m_{i j}=$ minor of $x_{i j}$ :
→
If $\text{A}=\begin{bmatrix} 3 & 4 \\ 2 & 4 \end{bmatrix},\text{B}=\begin{bmatrix} -2 & -2 \\ 0 & -1 \end{bmatrix}$ then (A + B)-1 =
  1. Is A akew-symmetric matrix.
  2. A-1 + B-1
  3. Does not exist.
  4. None of these.
→
The number of functions $f :\{1,2,3,4\} \rightarrow\{ a \in Z :| a | \leq 8\}$ satisfying $f ( n )+$ $\frac{1}{ n } f ( n +1)=1, \forall n \in\{1,2,3\}$ is
→
The first step in formulating an LP problem is:
  1. Graph the problem.
  2. Perform a sensitivity analysis.
  3. Identify the objective and the constraints.
  4. Define the decision variables.
  5. Understand the managerial problem being faced.
→