lim mendekati 0 cos x-1/cos 2x-1
Matematika
treshop2k16
Pertanyaan
lim mendekati 0 cos x-1/cos 2x-1
1 Jawaban
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1. Jawaban whongaliem
limit (cos x - 1) / (cos 2x - 1) = limit (cos x -1) / (cos² x - sin² x - 1)
x⇒0 x⇒0
= limit (cos x - 1) / (cos² x - (1 - cos² x) - 1)
x⇒0
= limit (cos x - 1) / (cos² x - 1 + cos² x - 1)
x⇒0
= limit (cos x - 1) / (2.cos² x - 2)
x⇒0
= limit (cos x - 1) / 2 (cos² x - 1)
x⇒0
= limit (cos x - 1) / 2 (cos x - 1)(cos x + 1)
x⇒0
= limit 1 / 2 (cos x + 1)
x⇒0
= 1 / 2 (cos 0° + 1)
= 1 / 2 (1 + 1)
= 1 / (2 .2)
= 1 / 4