Q70 / 160 · TS EAMCET 2017 · Mathematics
$\lim _{y \rightarrow 1}\left(\frac{1}{y^2-1}-\frac{2}{y^4-1}\right)=$
- Correct answerA$\frac{1}{2}$
- B$\frac{1}{3}$
- C$\frac{1}{4}$
- D0
Solution
We have, $\lim _{y \rightarrow 1}\left(\frac{1}{y^2-1}-\frac{2}{y^4-1}\right)$
$$
\begin{aligned}
& =\lim _{y \rightarrow 1}\left(\frac{y^2+1-2}{y^4-1}\right) \\
& =\lim _{y \rightarrow 1}\left(\frac{y^2-1}{\left(y^2-1\right)\left(y^2+1\right)}\right) \\
& =\lim _{y \rightarrow 1} \frac{1}{y^2+1}=\frac{1}{1+1}=\frac{1}{2}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.