If f(x) = l x 1 x , , ,x 0 , , , , , , , , , , , ,k, , ,x = 0 . i… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}x\sin \frac{1}{x},\,\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,k,\,\,x = 0\end{array} \right.$ is continuous at $x = 0$, then the value of $k$ is

A
$1$
B
$-1$
C
$0$
D
$2$

✓

Answer

If function $f(x)$ is continuous at $x = 0,$ then
$f(0) = \mathop {\lim }\limits_{x \to 0} \,f(x)$
Given $f(0) = k ; f(0) = k = \mathop {\lim }\limits_{x \to 0} \,x\,\left( {\sin \frac{1}{x}} \right)$
$f(0) = k = 0,{\rm{ }}\left( { - 1 \le \sin \frac{1}{x} \le 1} \right)$;
$\therefore k = 0$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If a dice is thrown twice, the probability of occurrence of $4$ at least once is

Let $A =\left\{ z \in C :\left|\frac{ z +1}{ z -1}<1\right|\right\}$ and $B =\left\{ z \in C : \arg \left(\frac{ z -1}{ z +1}\right)=\frac{2 \pi}{3}\right\}$ Then $A \cap B$ is

The equation to the straight line passing through the point of intersection of the lines $5x - 6y - 1 = 0$ and $3x + 2y + 5 = 0$ and perpendicular to the line $3x - 5y + 11 = 0$ is

Let $F(\alpha ) = \left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }&0\\{\sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]$, where $\alpha \in R.$ Then ${[F(\alpha )]^{ - 1}}$ is equal to

The probabilities that a student passes in Mathematics, Physics and Chemistry are $m, p$ and $c$ respectively. On these subjects, the student has a $75\%$ chance of passing in at least one, a $50\%$ chance of passing in at least two and a $40\%$ chance of passing in exactly two. Which of the following relations are true

The equation $\sqrt {(x + 1)} - \sqrt {(x - 1)} = \sqrt {(4x - 1)} $ has

Let for some function $y=f(x), \int_{0}^{x} t f(t) d t=x^{2} f(x)$, $x>0$ and $f(2)=3$. Then $f(6)$ is equal to :

The value of $\mathop {\lim }\limits_{n \to \infty } \cos \left( {\frac{x}{2}} \right)\cos \left( {\frac{x}{4}} \right)\cos \left( {\frac{x}{8}} \right)...\cos \left( {\frac{x}{{{2^n}}}} \right)$ is

The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ is

The solution of the differential equation, $2\, x^2y \frac{{dy}}{{dx}} = \tan (x^2y^2) - 2xy^2$ given $y(1) = \sqrt {\frac{\pi }{2}} $ is