Pertanyaan

Nilai x → 4 π lim ( sin x − cos x cos 2 x ) = ....

Nilai $x \to \frac{π}{4} lim (\frac{cos 2 x}{sin x - cos x}) = ....$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

Jawaban yang benar adalah A

Pembahasan

Limit trigonometri. lim x → 4 π ( s i n x − c o s x c o s 2 x ) = = = = = = = = lim x → 4 π ( s i n x − c o s x c o s 2 x − s i n 2 x ) lim x → 4 π ( s i n x − c o s x ( c o s x − s i n x ) ( c o s x + s i n x ) ) lim x → 4 π ( − ( c o s x − s i n x ) ( c o s x − s i n x ) ( c o s x + s i n x ) ) lim x → 4 π − ( cos x + sin x ) lim x → 4 π − cos x − sin x − cos 4 π − sin 4 π − 2 1 2 − 2 1 2 − 2 Jadii, x → 4 π lim (( s i n x − c o s x c o s 2 x )) = − 2 Oleh karena itu, Jawaban yang benar adalah A

Limit trigonometri.

$lim_{x \to \frac{π}{4}} (\frac{c o s 2 x}{s i n x - c o s x}) = = = = = = = = lim_{x \to \frac{π}{4}} (\frac{c o s ^{2} x - s i n ^{2} x}{s i n x - c o s x}) lim_{x \to \frac{π}{4}} (\frac{( c o s x - s i n x ) ( c o s x + s i n x )}{s i n x - c o s x}) lim_{x \to \frac{π}{4}} (\frac{( c o s x - s i n x ) ( c o s x + s i n x )}{- ( c o s x - s i n x )}) lim_{x \to \frac{π}{4}} - (cos x + sin x) lim_{x \to \frac{π}{4}} - cos x - sin x - cos \frac{π}{4} - sin \frac{π}{4} - \frac{1}{2} 2 - \frac{1}{2} 2 - 2$