MCQ
$\mathop {\lim }\limits_{y \to 0} \frac{{\sqrt {1 + \sqrt {1 + {y^4}} } - \sqrt 2 }}{{{y^4}}} = $
- ✓$\frac{1}{{4\sqrt 2 }}$
- B$\frac{1}{{2\sqrt 2 \left( {\sqrt 2 + 1} \right)}}$
- C$\frac{1}{{2\sqrt 2 }}$
- Dઅસ્તિત્વ ધરાવે નહીં
So, $\sqrt {1 + {y^4}} = 1 + \frac{{{y^4}}}{2}$
$\mathop {\lim }\limits_{y \to 0} \frac{{\sqrt {2 + \frac{{{y^4}}}{2}} - \sqrt 2 }}{{{y^4}}}$
$ = \frac{{\sqrt 2 \left( {1 + \frac{{{y^4}}}{8} - 1} \right)}}{{{y^4}}} = \frac{{\sqrt 2 }}{8} = \frac{1}{{4\sqrt 2 }}$
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