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x → 0 lim sin 2 x − cos 2 x + 1 x tan x = ...

$x \to 0 lim \frac{x tan x}{sin ^{2} x - cos 2 x + 1} = ...$

3
$begin mathsize 12px style fraction numerator square root of 3 over denominator 3 end fraction end style$
$begin mathsize 12px style fraction numerator square root of 3 over denominator 2 end fraction end style$

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$size 12px lim with size 12px x size 12px rightwards arrow size 12px 0 below square root of fraction numerator size 12px x size 12px space size 12px tan size 12px space size 12px x over denominator size 12px sin to the power of size 12px 2 size 12px space size 12px x size 12px minus size 12px cos size 12px space size 12px 2 size 12px x size 12px plus size 12px 1 end fraction end root size 12px equals size 12px lim with size 12px x size 12px rightwards arrow size 12px 0 below square root of fraction numerator size 12px x size 12px space size 12px tan size 12px space size 12px x over denominator size 12px sin to the power of size 12px 2 size 12px space size 12px x size 12px minus open parentheses size 12px 1 size 12px minus size 12px 2 size 12px space size 12px sin to the power of size 12px 2 size 12px space size 12px x close parentheses size 12px plus size 12px 1 end fraction end root size 12px equals size 12px lim with size 12px x size 12px rightwards arrow size 12px 0 below square root of fraction numerator size 12px x size 12px space size 12px tan size 12px space size 12px x over denominator size 12px sin to the power of size 12px 2 size 12px space size 12px x size 12px plus size 12px 2 size 12px space size 12px sin to the power of size 12px 2 size 12px space size 12px x size 12px minus size 12px 1 size 12px plus size 12px 1 end fraction end root size 12px equals size 12px lim with size 12px x size 12px rightwards arrow size 12px 0 below square root of fraction numerator size 12px x size 12px space size 12px tan size 12px space size 12px x over denominator size 12px 3 size 12px space size 12px sin to the power of size 12px 2 size 12px space size 12px x end fraction end root size 12px equals size 12px lim with size 12px x size 12px rightwards arrow size 12px 0 below square root of fraction numerator horizontal strike size 12px x size 12px space size 12px tan size 12px space size 12px x end strike over denominator size 12px 3 size 12px space horizontal strike size 12px sin size 12px space size 12px x end strike size 12px. horizontal strike size 12px sin size 12px space size 12px x end strike end fraction end root size 12px equals square root of size 12px 1 over size 12px 3 end root size 12px equals size 12px 1 over size 12px 3 square root of size 12px 3$

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