Question

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lim x->0 √(1+xsin8x) - 1 / tg^2(2x)

Answer 1

$lim_{x to 0} frac{ sqrt{1+xsin8x}-1 }{tg^22x} = lim_{x to 0} frac{ frac{sin8x+8xcos8x}{2sqrt{1+xsin8x}} }{ frac{4tg2x}{cos^22x} } = lim_{x to 0} frac{ frac{sin8x+8xcos8x}{2} }{ frac{4tg2x}{1} }$$= lim_{x to 0} frac{sin8x+8xcos8x}{8tg2x} = lim_{x to 0} frac{16cos8x - 64xsin8x}{ frac{16}{cos^22x} } = frac{16}{16} = 1$