MCQ
$\mathop {\lim }\limits_{x \to \frac{{{\pi ^ + }}}{2}} {e^{\left[ {cotx} \right]}}$ is equal to :-
(where $[.]$ is greatest integer function)
  • A
    $e$
  • B
    $1$
  • C
    $0$
  • $\frac{1}{e}$

Answer

Correct option: D.
$\frac{1}{e}$
d

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

Similar questions

Let the functions $f: R \rightarrow R$ and $g : R \rightarrow R$ be defined by$f(x)=e^{x-1}-e^{-|x-1|}$ and  $g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right) \text {. }$ Then the area of the region in the first quadrant bounded by the curves $y=f(x), y=g(x)$ and $x=0$ is
The population $P = P ( t )$ at time ${ }^{\prime} t ^{\prime}$ of a certain species follows the differential equation $\frac{ dP }{ dt }=0.5 P -450 .$ If $P (0)=850,$ then the time at which population becomes zero is
Area enclosed by the curve $y = f(x)$ that is being defined parametrically as $x = \frac{{1 - {t^2}}}{{1 + {t^2}}},\,y = \frac{{2t}}{{1 + {t^2}}}$ (where $t \in R$ ) is equal to
If the co-efficient of $x^9$ in $\left(\alpha x^3+\frac{1}{\beta x}\right)^{11}$ and the co-efficient of $x^{-9}$ in $\left(\alpha x-\frac{1}{\beta x^3}\right)^{11}$ are equal, then $(\alpha \beta)^2$ is equal to $.............$.
The function $L(x) = \int_1^x {\frac{{dt}}{t}} $ satisfies the equation
An integrating factor for the differential equation $(1 + {y^2})dx - ({\tan ^{ - 1}}y - x)dy = 0$
If $\frac{{5\pi }}{2} < x < 3\pi $, then the value of the expression $\frac{{\sqrt {1 - \sin x}  + \sqrt {1 + \sin x} }}{{\sqrt {1 - \sin x}  - \sqrt {1 + \sin x} }}$ is
Let a set $A=A_{1} \cup A_{2} \cup \ldots \cup A_{k,} \quad$ where $A_{ i } \cap A _{ j }=\phi$ for $i \neq j 1 \leq i , j \leq k$. Define the relation $R$ from $A$ to $A$ by $R=\left\{(x, y): y \in A_{i}\right.$ if and only if $\left.x \in A_{i}, 1 \leq i \leq k\right\}$. Then, $R$ is
The value of $\sin \frac{\pi }{{16}}\sin \frac{{3\pi }}{{16}}\sin \frac{{5\pi }}{{16}}\sin \frac{{7\pi }}{{16}}$ is
Which of the following equation is non-linear