Mathematics | TS EAMCET 2017 | Discussion Page

1)

$\lim_{y \rightarrow1}\left(\frac{1}{y^{2}-1}-\frac{2}{y^{4}-1}\right)=$

A)

$\frac{1}{2}$

B)

$\frac{1}{3}$

C)

$\frac{1}{4}$

D) 0

Option A

We have,

$\lim_{y \rightarrow1}\left(\frac{1}{y^{2}-1}-\frac{2}{y^{4}-1}\right)=$

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

$=\lim_{y \rightarrow 1}\left(\frac{y^{2}-1}{(y^{2}-1)(y^{2}+1)}\right)$

$=\lim_{y \rightarrow 1}\frac{1}{y^{2}+1}=\frac{1}{1+1}=\frac{1}{2}$

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