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Jawaban Terkonfirmasi

Lim (3x) / (√(9 + x) – √(9 – x)) . (√(9 + x) + √(9 – x))/(√(9 + x) + √(9 – x))
x=>0

Lim 3x (√(9 + x) + √(9 – x)) / ((9 + x) – (9 – x))
x=>0

Lim 3x (√(9 + x) + √(9 – x)) / (2x)
x=>0

Lim 3/2 (√(9 + x) + √(9 – x))
x=>0

= 3/2 (√(9 + 0) + √(9 – 0)

= 3/2 (3 + 3)

= 9

Jawaban Terkonfirmasi

$displaystyle lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}=lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}cdotfrac{sqrt{9+x}+sqrt{9-x}}{sqrt{9+x}+sqrt{9-x}}\lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}=lim_{xto0}frac{3x(sqrt{9+x}+sqrt{9-x})}{9+x-9+x}\lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}=lim_{xto0}frac{3x(sqrt{9+x}+sqrt{9-x})}{2x}\lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}=lim_{xto0}frac{3(sqrt{9+x}+sqrt{9-x})}{2}$
$displaystyle lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}=frac{3(sqrt{9+0}+sqrt{9-0})}{2}\lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}=frac{3(3+3)}{2}\lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}=3(3)\boxed{boxed{lim_{xto0}frac{3x}{sqrt{9+x}-sqrt{9-x}}=9}}$