lim _{x rightarrow 0} frac{x tan 2 x-2 x tan | vedclass

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Question

(C) हमारे पास व्यंजक $L = \lim _{x ightarrow 0} \frac{x 	an 2 x-2 x 	an x}{(1-\cos 3 x)(\operatorname{cosec} x-\cot x)^2}$ है।सबसे पहले,हर के पद $

Vedclass · Accepted Answer

$\frac{16}{9}$

Vedclass · Answer

(C) हमारे पास व्यंजक $L = \lim _{x ightarrow 0} \frac{x 	an 2 x-2 x 	an x}{(1-\cos 3 x)(\operatorname{cosec} x-\cot x)^2}$ है।सबसे पहले,हर के पद $(\operatorname{cosec} x-\cot x) = \frac{1-\cos x}{\sin x} = 	an(x/2)$ को सरल करें।अतः,$(\operatorname{cosec} x-\cot x)^2 = 	an^2(x/2) \approx \frac{x^2}{4}$ जब $x ightarrow 0$ हो।साथ ही,$1-\cos 3x = 2 \sin^2(\frac{3x}{2}) \approx \frac{9x^2}{2}$।हर $\frac{9x^2}{2} \cdot \frac{x^2}{4} = \frac{9x^4}{8}$ हो जाता है।अब,अंश को सरल करें: $x 	an 2x - 2x 	an x = 2x^4$।अतः,$L = \lim _{x ightarrow 0} \frac{2x^4}{9x^4/8} = \frac{16}{9}$।

$\lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 3 x)(\operatorname{cosec} x-\cot x)^2}=$

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