MCQ
The function $f (x) =$ $\mathop {Lim}\limits_{n \to \infty } \,\,\frac{{{x^{2n}} - 1}}{{{x^{2n}} + 1}}$ is identical with the function
- A$g (x) = sgn(x - 1)$
- B$h (x) = sgn (tan^{-1}x)$
- ✓$u (x) = sgn( | x | - 1)$
- D$v (x) = sgn (cot^{-1}x)$
✓
Answer
Correct option: C.
$u (x) = sgn( | x | - 1)$
c
$f (x) =$$\left[ \begin{gathered} \hfill \\ \hfill \\ \hfill \\ \hfill \\ \end{gathered} \right.$ $\begin{gathered} - 1\,\,\,\,\,\,if\,\, - 1 < x < 1 \hfill \\ \hfill \\ \,\,\,0\,\,\,\,\,\,if\,\,x = 1\,\,or\,\, - 1 \hfill \\ \hfill \\ \,\,\,1\,\,\,\,\,\,if\,\,|x| > 1 \hfill \\ \end{gathered} $ and $g (x) = sgn(|x| - 1)$ is same
$f (x) =$$\left[ \begin{gathered} \hfill \\ \hfill \\ \hfill \\ \hfill \\ \end{gathered} \right.$ $\begin{gathered} - 1\,\,\,\,\,\,if\,\, - 1 < x < 1 \hfill \\ \hfill \\ \,\,\,0\,\,\,\,\,\,if\,\,x = 1\,\,or\,\, - 1 \hfill \\ \hfill \\ \,\,\,1\,\,\,\,\,\,if\,\,|x| > 1 \hfill \\ \end{gathered} $ and $g (x) = sgn(|x| - 1)$ is same
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The sum of the series
→$\frac{3}{{1! + 2! + 3!}} + \frac{4}{{2! + 3! + 4!}} + \frac{5}{{3! + 4! + 5!}} + ...... + \frac{{2008}}{{\left( {2006} \right)! + \left( {2007} \right)! + \left( {2008} \right)!}}$ is equal to
Number of odd numbers of five distinct digits can be formed by the digits $0, 1, 2, 3, 4,$ is:
→A company produces on an average $4000$ items per month for the first $3$ months. How many items it must produce on an average per month over the next $9$ months, to average $4375$ items per month over the whole?
→The term independent of $y$ in the expansion of ${({y^{ - 1/6}} - {y^{1/3}})^9}$ is
→Consider $10$ observation $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}$. such that $\sum_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum_{i=1}^{10}\left(x_i-\beta\right)^2=40$, where $\alpha, \beta$ are positive integers. Let the mean and the variance of the observations be $\frac{6}{5}$ and $\frac{84}{25}$ respectively. The $\frac{\beta}{\alpha}$ is equal to :
→The number of way to sit $3$ men and $2 $ women in a bus such that total number of sitted men and women on each side is $3$
→If graph of $y = ax^2 -bx + c$ is following, then sign of $a$, $b$, $c$ are
→There are $10$ engineering colleges and five students $A, B, C, D, E$ . Each of these students got offer from all of these $10$ engineering colleges. They randomly choose college independently of each other. Tne probability that all get admission in different colleges can be expressed as $\frac {a}{b}$ where $a$ and $b$ are co-prime numbers then the value of $a + b$ is
→The position of a moving point in the $XY$ -plane at time $t$ is given by $\left( {(u\cos \alpha )t,(u\sin \alpha )t - \frac{1}{2}g{t^2}} \right),$ where $u,\,\alpha ,\,g$ are constants. The locus of the moving point is
→Four distinct points $(2k,\,3k),(1,0),(0,1)$ and $(0,0)$ lie on a circle for
→