Download App

CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY1 Mark
MCQ
The function $\text{f(x)}=\frac{\text{x}^3+\text{x}^2-16\text{x}+20}{\text{x}-2}$ is not defind for $x = 2$. in order to make $f(x)$ continuous at $x = 2$, here $f(2)$ should be defined as:
  • ✓
    $0$
  • B
    $1$
  • C
    $2$
  • D
    $3$
✓

Answer

Correct option: A.
$0$
Here,
$x^3+ x^2- 16x + 20$
$= x^3- 2x^2+ 3x^2- 6x - 10x + 20$
$= x^2(x - 2) + 3x(x - 2) - 10(x - 2)$
$= (x - 2)(x^2+ 3x - 10)$
$= (x - 2)(x - 2) (x - 5)$
$= (x - 2)^2(x + 5)$
So, the given function can be rewritten as
$\text{f(x)}=\frac{(\text{x}-2)^2(\text{x}+5)}{\text{x}-2}$
$\Rightarrow\text{f(x)}=(\text{x}-2)(\text{x}+5)$
If $f(x)$ is continuous at $x = 2$, then
$\lim\limits_{\text{x}\rightarrow2}\text{f(x)}=\text{f}(2)$
$\Rightarrow\lim\limits_{\text{x}\rightarrow2}(\text{x}-2)(\text{x}+5)=\text{f}(2)$
$\Rightarrow\text{f}(2)=0$
Hence, in order to make $f(x)$ continuous at $x = 2, f(2)$ should be defined as $0$.

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 "M.C.Q (1 Marks)" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\mathrm{y}=\mathrm{y}(\mathrm{x})$ be the solution of the differential equation $\frac{d y}{d x}=2(y+2 \sin x-5) x-2 \cos x$ such that $\mathrm{y}(0)=7$. Then $\mathrm{y}(\pi)$ is equal to :
→
Let $S$ be the set of all twice differentiable functions $f$ from $R$ to $R$ such that $\frac{d^2 f}{d x^2}(x)>0$ for all $x \in(-1,1)$. For $f \in S$, let $X_f$ be the number of points $x \in(-1,1)$ for which $f(x)=x$. Then which of the following statements is(are) true?

($A$) There exists a function $f \in S$ such that $X_f=0$

($B$) For every function $f \in S$, we have $X_f \leq 2$

($C$) There exists a function $f \in S$ such that $X_f=2$

($D$) There does $NOT$ exist any function $f$ in $\mathrm{S}$ such that $\mathrm{X}_f=1$

→
The sum of the distinct real values of $\mu $, for which the vectors, $\mu \hat i + \hat j + \hat k,\,\hat i + \mu \hat j + \hat k,\,\hat i + \hat j + \mu \hat k$ are co-planar, is
→
$\int_0^\infty {{e^{ - 2x}}(\sin 2x + \cos 2x)\,dx = } $
→
The area bounded by the curves $\text{y}=\sin\text{x},\text{y}=\cos\text{x}$ y − axes in first quadrant is:
→
Corner points of the bounded feasible region for an $LP$ problem are $(0,4),(6,0),(12,0),(12,16)$ and $(0,10) .$

Let $z=8 x+12 y$ be the objective function. Match the following :

$(i)$ Minimum value of $z$ occurs at $\ldots$

$(ii)$ Maximum value of $z$ occurs at $\ldots$

$(iii)$ Maximum of $z$ is $\ldots$

$(iv)$ Minimum of $z$ is $\ldots \ldots$

→
Choose the correct answer from given four options in each of the Exercise $:$ If $A$ and $B$ are invertible matrices, then which of the following is not correct?
→
Which of the following set of points are non- collinear
→
Unit vectors  $ a, b$  and $ c$  are coplanar. A unit vector $d $ is perpendicular to them. If $(a \times b) \times (c \times d) = \frac{1}{6}i - \frac{1}{3}j + \frac{1}{3}k$ and the angle between $ a$  and $ b $ is ${30^o}$, then  $ c $ is
→
Differential coefficient of ${\sec ^{ - 1}}\frac{1}{{2{x^2} - 1}}w.r.t$ $\sqrt {1 - {x^2}} $ at $x = \frac{1}{2}$ is
→