Limit _ x , ^ - 1 ( x + 1 , , - , x ) ^ - 1 ( 2x + 1 x - 1 ) ^x i… - Vidyadip

MCQ

$\mathop {Limit}\limits_{x \to \infty } \,\frac{{{{\cot }^{ - 1}}\left( {\sqrt {x + 1} \,\, - \,\sqrt x } \right)}}{{{{\sec }^{ - 1}}\left\{ {{{\left( {\frac{{2x + 1}}{{x - 1}}} \right)}^x}} \right\}}}$ is equal to

✓
$1$
B
$0$
C
$\pi /2$
D
non existent

✓

Answer

Correct option: A.

$1$

a
$\mathop {Limit}\limits_{x \to \infty } \,\sqrt {x + 1} \, - \sqrt x \,$ $= 0$ $\Rightarrow cot^{-1}(0) = \pi /2$
$\mathop {Limit}\limits_{x \to \infty } \,{\left( {\frac{{2x + 1}}{{x - 1}}} \right)^x}\,\, = \,\,\infty \,$ $\Rightarrow\,\,\, sec^{-1} (\infty ) = \pi /2$

$\therefore\,\, l = 1$ Ans

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

Four fair dice are thrown independently $27$ times. Then the expected number of times, at least two dice show up a three or a five, is

A straight line through the point $(1, 1)$ meets the $x$-axis at ‘$A$’ and the $y$-axis at ‘$B$’. The locus of the mid-point of $AB$ is

The locus of the centers of the circles which cut the circles $x^2 + y^2 + 4x - 6y + 9 = 0$ and $x^2 + y^2 - 5x + 4y - 2 = 0$ orthogonally is

Let $(x, y)$ be any point on the parabola $y^2=4 x$. Let $P$ be the point that divides the line segment from $(0,0)$ to $(x, y)$ in the ratio $1: 3$. Then the locus of $P$ is

The angle between the lines $x\cos {\alpha _1} + y\sin {\alpha _1} = {p_1}$ and $x\cos {\alpha _2} + y\sin {\alpha _2} = {p_2}$is

If the function $f:(-\infty,-1] \rightarrow(a, b]$ defined by $f(x)=e^{x^3-3 x+1}$ is one-one and onto, then the distance of the point $\mathrm{P}(2 \mathrm{~b}+4, \mathrm{a}+2)$ from the line $x+e^{-3} y=4$ is :

If the resultant of two forces of magnitudes $ P $ and $Q$ acting at a point at an angle of ${60^o}$ is $\sqrt 7 Q,$ then $P/Q$ is

The equation of the straight line which is perpendicular to $y = x$ and passes through $(3, 2)$ is

If $\vec a = 2\hat i + \hat j + \hat k,\vec b = \hat i + 2\vec j + 2\vec k,\vec c = \vec i + \vec j + 2\hat k$ and $\left( {1 + \alpha } \right)\hat i + \beta \left( {1 + \alpha } \right)\hat j + \gamma \left( {1 + \alpha } \right)\left( {1 + \beta } \right)\hat k = \hat a \times \left( {\vec b \times \vec c} \right)$ , then $\alpha ,\beta ,\gamma $ are

If equation of three sides of a triangle are $x = 2,$ $y + 1 = 0$ and $x + 2y = 4$ then co-ordinates of circumcentre of this triangle are