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
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.