Question

$\displaystyle\lim_{y \to 1} \left( \frac{1}{y^2 - 1} - \frac{2}{y^4 - 1} \right) = $

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. 0

Answer 1

Answer: (A)

We have, $\displaystyle \lim _{y \rightarrow 1}\left(\frac{1}{y^{2}-1}-\frac{2}{y^{4}-1}\right)$
$=\displaystyle\lim _{y \rightarrow 1}\left(\frac{y^{2}+1-2}{y^{4}-1}\right)$
$=\displaystyle\lim _{y \rightarrow 1}\left(\frac{y^{2}-1}{\left(y^{2}-1\right)\left(y^{2}+1\right)}\right)$
$=\displaystyle\lim _{y \rightarrow 1} \frac{1}{y^{2}+1}=\frac{1}{1+1}=\frac{1}{2}$