Function f(x) = x^2 - 1 x^3 - 1 is not defined at x = 1, then the… - Vidyadip

MCQ

Function $f(x) = \frac{{{x^2} - 1}}{{{x^3} - 1}}$is not defined at $x = 1$, then the value of $f(1)$ when function is continuous at $x = 1$, will be

A
$ - \frac{3}{2}$
✓
$\frac{2}{3}$
C
$\frac{3}{2}$
D
$ - \frac{2}{3}$

✓

Answer

Correct option: B.

$\frac{2}{3}$

b
(b) $f(x) = \frac{{{x^2} - 1}}{{{x^3} - 1}} = \frac{{(x - 1)\,(x + 1)}}{{(x - 1)\,({x^2} + x + 1)}}\, \Rightarrow f(1) = \frac{2}{3}$.

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

Choose the correct answers from the given four options:The value of $c$ in Rolle’s theorem for the function $f(x) = x^3 - 3x$ in the interval $\big[0,\sqrt{3}\big]$ is:

Order of $\Big( \frac{\text{dy}}{\text{dx}}\Big)^{3}+ \Big( \frac{\text{dy}}{\text{dx}}\Big)^{2}+\text{y}^{4}=0$ is :

The corner points of the feasible region are $A(3,3), B(20,3), C(20,10), D(18,12)$ and $E(12, 12)$. The maximum value of $Z=2 x+3 y$ is $.......$

If $A$ is a square matrix of order $3$ such that the value of $|\operatorname{adj} A|=8$, then the value of $\left|A^{\top}\right|$ is

Let $f$ be a function defined on the set of all positive integers such that $f(x y)=f(x)+f(y)$ for all positive integers $x, y$. If $f(12)=24$ and $f(8)=15$. The value of $f(48)$ is

The function $\text{f(x)=}\begin{cases}\frac{\text{e}\frac{1}{\text{x}}-1}{\text{e}\frac{1}{\text{x}}+1},&\text{x}\neq0\\0,&\text{x}=0\end{cases}$

Choose the correct answer from the given four options. For any vector $\vec{\text{a}},$ the value of $(\vec{\text{a}}\times\hat{\text{i}})^2+(\vec{\text{a}}\times\hat{\text{j}})^2+(\vec{\text{a}}\times\hat{\text{k}})^2$ is :

If the set $A$ contains $5$ elements and the set $B$ contains $6$ elements, then the number of one$-$one and onto mappings from $A$ to $B$ is:

If $R = \{(6, 6), (9, 9), (6, 12), (12, 12), (12,6)\}$ is a relation on set $A = \{3, 6, 9, 12\}$ , then relation $R$ is

Let a curve $y=f(x)$ pass through the point $\left(2,\left(\log _{e} 2\right)^{2}\right)$ and have slope $\frac{2 y}{x \log _{e} x}$ for all positive real value of $x$. Then the value of $f(e)$ is equal to $.....$