limy→ 0[frac√(1-y²)-√(1+y²)y²]

7.3 Q.I · Q39

\displaystyle\lim_{y\to 0}\left[\frac{\sqrt{1-y^2}-\sqrt{1+y^2}}{y^2}\right]

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Multiply by the conjugate $\sqrt{1-y^2}+\sqrt{1+y^2}$ : numerator becomes $(1-y^2)-(1+y^2)=-2y^2$ . So the expression is $\dfrac{-2y^2}{y^2(\sqrt{1-y^2}+\sqrt{1+y^2})}=\dfrac{-2}{\sqrt{1-y^2}+\sqr …

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Q. $\displaystyle\lim_{y\to 0}\left[\frac{\sqrt{1-y^2}-\sqrt{1+y^2}}{y^2}\right]$

Concept understanding — Limits by Rationalization

Q.lim⁡y→0[1−y2−1+y2y2]\displaystyle\lim_{y\to 0}\left[\frac{\sqrt{1-y^2}-\sqrt{1+y^2}}{y^2}\right]y→0lim​[y21−y2​−1+y2​​]

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Q. $\displaystyle\lim_{y\to 0}\left[\frac{\sqrt{1-y^2}-\sqrt{1+y^2}}{y^2}\right]$

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