Let p = lim_x → 0^+ (1 + tan^2 √(x))^1/2x, then log p is equal to

Let p = lim_x → 0^+ (1 + tan^2 √(x))^1/2x, then log p is… — JEE Main 2016 Mathematics PYQ

JEE Main 2016

Let

p = \lim_{x \to 0^+} (1 + \tan^2 \sqrt{x})^{1/2x}

, then

\log p

is equal to

Show answer and solution

Correct option: C

Solution

Take log: log p = lim(x→0⁺) (1/2x) · ln(1 + tan²√x).

As x→0⁺, tan²√x ≈ x, so ln(1 + tan²√x) ≈ tan²√x ≈ x.

Thus log p = lim(x→0⁺) x/(2x) = 1/2.

[JEE Main 2016]

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