Download App

STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
$\mathop {{\rm{lim}}}\limits_{x \to 2} \left( {\frac{{\sqrt {1 - {\rm{cos}}\left\{ {2\left( {x - 2} \right)} \right\}} }}{{x - 2}}} \right)=$
  • A
    $\sqrt 2 $
  • B
    -$\;\sqrt 2 $
  • C
    $\frac{1}{{\sqrt 2 }}$
  • ✓
    does not exist
✓

Answer

Correct option: D.
does not exist
d
$\mathop {\lim }\limits_{x \to 2} \frac{{\sqrt {1 - \cos \{ 2(x - 2)\} } }}{{x - 2}}$

$ = \mathop {\lim }\limits_{x \to 2} \frac{{\sqrt 2 |\sin (x - 2)|}}{{x - 2}}$

$R.H.L. = \mathop {\lim }\limits_{x \to {2^ - }} \frac{{\sqrt 2 \sin (x - 2)}}{{(x - 2)}} =  - \sqrt 2 $

$R.H.L. = \mathop {\lim }\limits_{x \to {2^ + }} \frac{{\sqrt 2 \sin (x - 2)}}{{(x - 2)}} =  - \sqrt 2 $

Thus $L . H . L . \neq R . H . L$

Hence, $\mathop {\lim }\limits_{x \to 2} \frac{{\sqrt {1 - \cos \{ 2(x - 2)\} } }}{{x - 2}}$ does not exist.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $R$ is a relation on the set $N$, defined by $\left\{ {\left( {x,y} \right);3x + 3y = 10} \right\}$

Statement $-1$ : $R$ is symmetric

Statement $-2$ : $R$ is reflexive

Statement $-3$ : $R$ is transitive, then thecorrect sequence of given statements is

(where $T$ means true and $F$ means false)

→
The value of $\int\limits_{ - \pi /2}^{\pi /2} {\frac{{dx}}{{\left[ x \right] + \left[ {\sin \,x} \right] + 4}}} $ where $[t]$ denotes the greatest integer less than or equal to $t$, is
→
$\int\limits_2^3 {\frac{{{{(x + 2)}^2}}}{{2{x^2} - 10x + 53}}} dx = $
→
If $\alpha ,\beta \ne 0$ and $f\left( n \right) = {\alpha ^n} + {\beta ^n}$ and $\left| {\begin{array}{*{20}{c}}3&{1 + f\left( 1 \right)}&{1 + f\left( 2 \right)}\\{1 + f\left( 1 \right)}&{1 + f\left( 2 \right)}&{1 + f\left( 3 \right)}\\{1 + f\left( 2 \right)}&{1 + f\left( 3 \right)}&{1 + f\left( 4 \right)}\end{array}} \right|\; = K{\left( {1 - \alpha } \right)^2}$ ${\left( {1 - \beta } \right)^2}{\left( {\alpha - \beta } \right)^2}$ ,then $K=$ . . . . . .
→
If $(x + iy)(p + iq) = ({x^2} + {y^2})i$, then
→
$x - 2 = {t^2},\;y = 2t$ are the parametric equations of the parabola
→
If $I=\int\limits_{1}^{2} \frac{d x}{\sqrt{2 x^{3}-9 x^{2}+12 x+4}},$ then
→
The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is -
→
The roots of the equation

$x^5 - 40x^4 + px^3 + qx^2 + rx + s = 0$ are in $G.P.$ The sum of their reciprocals is $10$. Then the value of $\left| s \right|$ is

→
$\mathop {\lim }\limits_{h \to 0} \frac{{{{(a + h)}^2}\sin (a + h) - {a^2}\sin a}}{h} = $
→