The function f(x) = 2 x^2 + 7 x^3 + 3 x^2 - x - 3 is discontinuou… - Vidyadip

MCQ

The function $f(x) = \frac{{2{x^2} + 7}}{{{x^3} + 3{x^2} - x - 3}}$ is discontinuous for

A
$x = 1$ only
B
$x = 1$ and $x = - 1$ only
✓
$x = 1,x = - 1,x = - 3$ only
D
$x = 1,x = - 1,x = - 3$ and other values of $x$

✓

Answer

Correct option: C.

$x = 1,x = - 1,x = - 3$ only

c
(c) $f(x) = \frac{{2{x^2} + 7}}{{{x^2}(x + 3) - 1(x + 3)}} = \frac{{2{x^2} + 7}}{{({x^2} - 1)(x + 3)}}$

$ = \frac{{2{x^2} + 7}}{{(x - 1)(x + 1)(x + 3)}}$

Hence points of discontinuity are

$x = 1$, $x = - 1$ and $x = - 3$ only.

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 $A$ and $B$ are such that $\text{P}(\text{A}\cup\text{B})=\frac{5}{9}$ and $\text{P}(\overline{\text{A}}\cup\overline{\text{B}})=\frac{2}{3},$ then $\text{P}(\overline{\text{A}})+\text{P}(\overline{\text{B}})=$

If $\int {\frac{{x + 1}}{{\sqrt {2x - 1} }}} dx = f\left( x \right)\,\sqrt {2x - 1} + C$ , where $C$ is a constant of integration of integration, then $f(x)$ is equal to

Let $A=\left[a_{i j}\right]$ be a square matrix of order $3$ such that $a_{i j}=2^{j-i}$, for all $i, j=1,2,3$. Then, the matrix $A ^{2}+ A ^{3}+\ldots+ A ^{10}$ is equal to

If $\int\limits_{a}^{x}{ty(t)dt={{x}^{2}}+y(x)}$ then $y$ as a function of $x$ is

Area of the region bounded by the curve $\text{y}=\sqrt{49-\text{x}^2}$ and the $x -$ axis is:

Evaluate$:\ \int\sec^2(7-4\text{x})\text{dx}.$

Evaluate $\begin{bmatrix}5&0&5\\1&4&3\\0&8&6\end{bmatrix}$ is:

The optimal value of the objective function is attained at the points

If the function $f(x) = {x^3} - 6a{x^2} + 5x$ satisfies the conditions of Lagrange's mean value theorem for the interval $[1, 2] $ and the tangent to the curve $y = f(x) $ at $x = {7 \over 4}$ is parallel to the chord that joins the points of intersection of the curve with the ordinates $x = 1$ and $x = 2$. Then the value of $a$ is

If in the interval $[0,3]$

$f\left( x \right) = \left\{ \begin{gathered} x{\left\{ x \right\}^2},x \notin I \hfill \\ x\,\,\,\,\,\,\,\,\,\,,x \in I \hfill \\ \end{gathered} \right.,$

then which of the following statement is correct?

(where $\{.\}$ denotes fractional part function)