Lim x = Π/41 - sin 2x / cos² 2xa. 1b. 1/2c. 1/2 √2d. √2e. 2

Lim x = Π/41 – sin 2x / cos² 2xa. 1b. 1/2c. 1/2 √2d. √2e. 2

Jawab:

1/2

Penjelasan dengan langkah-langkah:

$lim_{x to frac{pi}{4}} frac{1-sin2x}{cos^22x}=frac{0}{0}~to~gunakan~l'hopital\\\lim_{x to frac{pi}{4}} frac{1-sin2x}{cos^22x}\\=lim_{x to frac{pi}{4}} frac{-2cos2x}{2cos2x.(-sin2x)(2)}\\=lim_{x to frac{pi}{4}} frac{1}{2sin2x}\\=frac{1}{2sin2(frac{pi}{4})}\\=frac{1}{2sin(frac{pi}{2})}\\=frac{1}{2}$