If f(x) = l ( x^2 /a) - a, ; ; when ;x < a ; ; ; ; ; ; ; ; ; ; ;0… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}({x^2}/a) - a,\;\;{\rm{when}}\;x < a\\\;\;\;\;\;\;\;\;\;\;\;0,\;\;{\rm{when}}\;x = a{\rm{,}}\\a - ({x^2}/a),\;\;{\rm{when\,\, }}x > a\end{array} \right.$ then

A
$\mathop {\lim }\limits_{x \to a} f(x) = a$
✓
$f(x)$ is continuous at $x = a$
C
$f(x)$ is discontinuous at $x = a$
D
None of these

✓

Answer

Correct option: B.

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

b
(b) $f(a) = 0$

$\mathop {\lim }\limits_{x \to a - } \,f(x) = \mathop {\lim }\limits_{x \to a - } \left( {\frac{{{x^2}}}{a} - a} \right) = \mathop {\lim }\limits_{h \to 0} \,\left\{ {\frac{{{{(a - h)}^2}}}{a} - a} \right\} = 0$

and $\mathop {\lim }\limits_{x \to a + } f(x) = \mathop {\lim }\limits_{h \to 0} \,\,\left\{ {a - \frac{{{{(a + h)}^2}}}{a}} \right\} = 0$

Hence it is continuous at $x = a$.

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 STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $u = {\tan ^{ - 1}}\left\{ {{{\sqrt {1 + {x^2}} - 1} \over x}} \right\}$ and $v = 2{\tan ^{ - 1}}x$, then ${{du} \over {dv}}$ is equal to

The projections of a line on the co-ordinate axes are $4, 6, 12$. The direction cosines of the line are

If a * b denote the bigger among a and b and if ab = (a * b) + 3, then 4.7 =

The equation of the normal to the curve $\text{y}=\text{x}+\sin\text{x}\cos\text{x}\text{ at }\text{x}=\frac{\pi}{2}$ is

If $A = \left[ {\begin{array}{*{20}{c}}
{ - 4}&{ - 1}\\
3&1
\end{array}} \right]$ , then the determinant of the matrix $\left( {{A^{2016}} - 2{A^{2015}} - {A^{2014}}} \right)$ is

$z = 10x + 25y$ subject to $0\leq\text{X}\leq3$ and $0\leq\text{X}\leq3,$ $\text{x}+\text{y}\leq5$ then the maximum value of $z$ is:

Let $a-2 b+c=1$

If $f(x)=\left|\begin{array}{lll}{x+a} & {x+2} & {x+1} \\ {x+b} & {x+3} & {x+2} \\ {x+c} & {x+4} & {x+3}\end{array}\right|,$ then

Let $A=\left[\begin{array}{lll}1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{array}\right], a, b \in R$. If for some $n \in N$, $A ^{ n }=\left[\begin{array}{ccc}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{array}\right]$ then $n + a + b$ is equal to $\dots\dots$

Consider $f(x) = \frac{{{x^2}}}{{1 + {x^3}}}$ ; $g(t) = \int {f(t)\,\,dt}$ . If $g(1) = 0$ then $g(x)$ equals

Let $\Delta$ be the area of the region $\left\{( x , y ) \in R ^2: x ^2+ y ^2 \leq 21, y ^2 \leq 4 x , x \geq 1\right\}$. Then $\frac{1}{2}\left(\Delta-21 \sin ^{-1} \frac{2}{\sqrt{7}}\right)$ is equal to