limit x mendekati 0 (1-cos^2x-cosxsin^2x) : (x^4)
Matematika
Nugrahanti1
Pertanyaan
limit x mendekati 0 (1-cos^2x-cosxsin^2x) : (x^4)
1 Jawaban
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1. Jawaban whongaliem
limit (1 - cos² x - cos x . sin² x ) x^4 =
x⇒0
= limit (sin² x + cos² x - cos² x - cos x .sin² x ) / x^4
x⇒0
= limit (sin² x - cos x .sin² x) / x^4
x⇒0
= limit {sin² x (1 - cos x)} / x^4
x⇒0
= limit sin² x {1 - (cos² 1/2x - sin² 1/2x)} / x^4
x⇒0
= limit sin² x ( 1 - cos² 1/2x + sin² 1/2x) / x^4
x⇒0
= limit sin² x (sin² 1/2x + sin² 1/2 x) / x^4
x⇒0
= limit sin² x . (2 .sin² 1/2 x) / x^4
x⇒0
= limit sin²x / x² . limit 2 . sin² 1/2x / x²
x⇒0 x⇒0
= 1² . 2 (1/2)²
= 1 . 2 . 1/4
= 1/2