Limit x->0 x tan 3x/1-cos6x

Limit x->0 x tan 3x/1-cos6x

Jawaban Terkonfirmasi

$lim_{x to .0} frac{x .tan 3x}{1 - cos 6x}$ = $lim_{x to .0} frac{x. tan 3x}{1 - ( cos^{2} 3x - sin^{2} 3x)}$
= $lim_{x to .0} frac{x. tan 3x}{1 - cos^{2} 3x + sin^{2} 3x}$
= $lim_{x to .0} frac{x. tan 3x}{ sin^{2} 3x + sin^{2} 3x}$
= $lim_{x to .0} frac{x. tan 3x}{2. sin^{2} 3x}$ … kalikan dgn x/x
= 1/2 $lim_{x to .0} frac{ x^{2} }{ xin^{2} 3x} . frac{tan 3x}{x}$
= 1/2 . (1/3)² . 3
= 1/2 . 1/9 . 3
= 1/6