If f(x)= ll 1 2 x^2, & x 0 0, & x=0 . , then - Vidyadip

MCQ

$\text {If } f(x)=\left\{\begin{array}{ll}\frac{1}{2} \sin x^2, & x \neq 0 \\0, & x=0\end{array}\right. \text {, then }$

A
$\lim _{x \rightarrow 0} f(x)=\frac{1}{2}$
B
$f (x)$ is discontinuous at $x=0$
✓
$f (x)$ is continuous at $x=0$
D
none of these

✓

Answer

Correct option: C.

$f (x)$ is continuous at $x=0$

(C)
$\lim _{x \rightarrow 0} f (x)=\lim _{x \rightarrow 0} \frac{1}{2} \sin x^2=0= f (0)$
$\therefore \quad f (x)$ is continuous at $x=0$.

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 "MCQ" from Continuity→Continuity — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $f (x)=\frac{1-\sin x}{(\pi-2 x)^2}$, when $x \neq \frac{\pi}{2}$ and $f \left(\frac{\pi}{2}\right)=\lambda$, then $f (x)$ will be continuous function at $x=\frac{\pi}{2}$, when $\lambda=$

$\tan 15^{\circ}=$

If $f (x)=\left\{\begin{array}{cc}x^* \sin \frac{1}{x} ; & x \neq 0 \\ 0 ; & x=0\end{array}\right.$ is continuous an $x=0$, then

If y + c = 0 is a tangent to the circle $x^2+y^2-6 x-2 y+1=0$ at (a, 4) then

If in a regular polygon, the number of diagonals are 54 , then the number of sides of the polygon are

The locus of the centre of the circle which cuts off intercepts of length 2a and 2b from X-axis and Y-axis respectively, is

The number of discontinuities in R for the function $f(x)=\frac{x-1}{x^3+6 x^2+11 x+6}$ is

$\lim _{x \rightarrow 0} \frac{\cos (\sin x)-1}{x^2}=$

The value of $\lim _{x \rightarrow 0}\left\{\frac{a^x+b^x+c^x}{3}\right\}^{1 / x}$ is

If the vertex of a parabola be at origin and directrix be x + 5 = 0 then its latus rectum is