If x→0lim[1+x1n(1+b2)]x1=2bsin2θ,b>0,where θ∈(−π,π], then the value of θ is (a)±4π (b) ±3π (c) ±6π (d) ±2π

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If _{{{x}{0}}}{[{1}+{x}{1}{n}{({1}+{b}^{{2}})}]}^{{{{1}}{{x}}}

Question

If $x \to 0 lim [1 + x 1 n (1 + b^{2})]^{\frac{1}{x}} = 2 b sin^{2} θ, b > 0$ ,where $θ \in (- π, π],$ then the value of $θ$ is (a) $\pm \frac{π}{4}$ (b) $\pm \frac{π}{3}$ (c) $\pm \frac{π}{6}$ (d) $\pm \frac{π}{2}$

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Lucas Discussed

x \to 0 lim [1 + x 1 n (1 + b^{2})]^{\frac{1}{x}} = 2 b sin^{2} θ, b > 0

,where

θ \in (- π, π],

then the value of

θ

is (a)

\pm \frac{π}{4}

(b)

\pm \frac{π}{3}

(c)

\pm \frac{π}{6}

(d)

\pm \frac{π}{2}

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Question Text

x \to 0 lim [1 + x 1 n (1 + b^{2})]^{\frac{1}{x}} = 2 b sin^{2} θ, b > 0

,where

θ \in (- π, π],

then the value of

θ

is (a)

\pm \frac{π}{4}

(b)

\pm \frac{π}{3}

(c)

\pm \frac{π}{6}

(d)

\pm \frac{π}{2}