tolong ya lim x^2-1 / √3x+4 - √x+2 x⇒-1
Matematika
romibrema
Pertanyaan
tolong ya
lim x^2-1 / √3x+4 - √x+2
x⇒-1
lim x^2-1 / √3x+4 - √x+2
x⇒-1
1 Jawaban
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1. Jawaban arsetpopeye
Lim (x^2 - 1)/(√(3x + 4) - √(x + 2))
= Lim (x^2 - 1)/(√(3x + 4) - √(x + 2)) . (√(3x+4)+√(x+2))/(√(3x+4)+√(x+ 2))
= Lim (x^2 - 1)(√(3x + 4) + √(x + 2)) / ((3x + 4) - (x + 2))
= Lim (x^2 - 1)(√(3x + 4) + √(x + 2)) / (2x + 2)
= Lim (x + 1)(x - 1)(√(3x + 4) + √(x + 2)) / 2(x + 1)
= Lim (x - 1)(√(3x + 4) + √(x + 2)) / 2
= (-1 - 1)(√(3(-1) + 4) + √(-1 + 2)) / 2
= -2 (√1 + √1) / 2
= -1 (2)
= -2