Lim x(√x+4 - 2) x->0 ----------------- = 1 - cos x
Matematika
yoseph18
Pertanyaan
Lim x(√x+4 - 2)
x->0 ----------------- =
1 - cos x
x->0 ----------------- =
1 - cos x
1 Jawaban
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1. Jawaban whongaliem
limit {x (√x + 4) - 2} / 1 - cos x = limit {x (√(x + 4) - 2} / {1 - (cos² 1/2 x - sin² 1/2 x)}
x⇒0 x⇒0
= limit {x (√x + 4) - 2} / (1 - cos² 1/2 x + sin² 1/2 x)
x⇒0
= limit {x (√(x + 4) - 2} / (sin² 1/2 x + sin² 1/2 x)
x⇒0
= limit {x (√(x + 4) - 2) / 2.sin² 1/2 x
x⇒0
= limit {x (√(x + 4) - 2} {√(x + 4) + 2} / {2.sin² 1/2 x (√(x + 4) + 2}
x⇒0
= limit { x (x + 4 - 4) / {2.sin² 1/2 x (√(x + 4) + 2 }
x⇒0
= limit x (x) / {2.sin² 1/2 x (√(x + 4) + 2}
x⇒0
= limit x² / {2 .sin² 1/2 x (√(x + 4) + 2}
x⇒0
= 1/2 .limit {x² / sin² 1/2 x } { 1 / √(x +4) + 2}
= 1/2 . {1 /(1/2)}² . 1 / {√(0 + 4) + 2 }
= 1/2 . 2² . 1 /(√4 + 2)
= 1/2 . 4 . 1 /(2 + 2)
= 1/2 . 4 . 1/4
= 1/2