If f(x) = l 1 + x^2 , , , , when , , ,0 x 1 1 - x , , ,, when , ,… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}1 + {x^2},\,\,\,{\rm{when\,\,}}\,0 \le x \le 1\\1 - x\,\,\,,{\rm{when\,\,}}\,\,x > 1\end{array} \right.$, then

A
$\mathop {\lim }\limits_{x \to {1^ + }} f(x) \ne 0$
B
$\mathop {\lim }\limits_{x \to {1^ - }} f(x) \ne 2$
✓
$f(x)$ is discontinuous at $x = 1$
D
None of these

✓

Answer

Correct option: C.

$f(x)$ is discontinuous at $x = 1$

c
(c) $\mathop {\lim }\limits_{x \to 1 + } f(x) = 0$ and $\mathop {\lim }\limits_{x \to 1 - } \,\,f(x) = \,\,1 + 1 = 2$

Hence $f(x)$ is discontinuous at $x = 1$.

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 $\text{F}:[1,\infty)\rightarrow[2,\infty)$ is given by $\text{f(x)}=\text{x}+\frac{1}{\text{x}},$ then $f^{-1}(x)$ equals:

The probability that a certain beginner at golf gets a good shot if he uses the correct club is $\frac{1}{3}$ and the probability of a good shot with an incorrect club is $\frac{1}{4}$. In his bag are $5$ different clubs, only one of which is correct for the shot in question. If he chooses a club at random and takes a stroke, then the probability that he gets a good shot, is

$\int_{ - 3}^3 {\frac{{{x^2}\sin 2x}}{{{x^2} + 1}}\,dx = } $

If $\int_{}^{} {\frac{{f(x)\;dx}}{{\log \sin x}} = \log \log \sin x} $, then $f(x) = $

Choose the correct answer from the given four options: The function $f(x) = 2x^3 - 3x^2 - 12x + 4,$ has:

$\int_{0}^{1}\text{x}(1-\text{x})^{99}$ is equal to:

The sum $\sum\limits_{n = 1}^\infty {{{\cot }^{ - 1}}} \left( {\frac{{2\left( {\sum\limits_{k = 1}^n k } \right) - 1}}{3}} \right)$ is equal to

Let $n \geq 2$ be a natural number and $f:[0,1] \rightarrow R$ be the function defined by

$f(x)= \begin{cases}n(1-2 n x) \text { if } 0 \leq x \leq \frac{1}{2 n}2 n(2 n x-1) \text { if } \frac{1}{2 n} \leq x \leq \frac{3}{4 n}4 n(1-n x) \text { if } \frac{3}{4 n} \leq x \leq \frac{1}{n} \\ \frac{n}{n-1}(n x-1) \text { if } \frac{1}{n} \leq x \leq 1\end{cases}$

If $n$ is such that the area of the region bounded by the curves $x=0, x=1, y=0$ and $y=f(x)$ is $4$ , then the maximum value of the function $f$ is

If the solution of the differential equation $(2 x+3 y-2) d x+(4 x+6 y-7) d y=0, y(0)=3$, is $\alpha x+\beta y+3 \log _e|2 x+3 y-\gamma|=6$, then $\alpha+2 \beta+3 \gamma$ is equal to

If $\omega $ is cube root of unity, then root of the equation $\left| {\begin{array}{*{20}{c}}
{x + 2}&\omega &{{\omega ^2}} \\
\omega &{x + 1 + {\omega ^2}}&1 \\
{{\omega ^2}}&1&{x + 1 + \omega }
\end{array}} \right| = 0$ is