Let p = then log p is equal to

Engineering

Mathematics

One to The Power Infinity Form

Question

Let p = $\underset{x \to 0^{+}}{Lim} {(1 + \tan \sqrt[2]{x})}^{\frac{1}{2 x}}$ then log p is equal to

$\frac{1}{2}$

$\frac{1}{4}$

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$p = \underset{x \to 0^{+}}{Lim} {(1 + \tan \sqrt[2]{x})}^{\frac{1}{2 x}} = e^{\underset{x \to 0^{+}}{Lim} \frac{1}{2 x} (\tan \sqrt[2]{x})} = e^{\frac{1}{2}}$

$∴ \log p = \frac{1}{2}$ .