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lim[3x-√(9x²-6)]
x→+∞
=lim[3x-√(9x²-6)][3x+√(9x²-6)]/[3x+√(9x²-6)]
x→+∞
=lim[(3x)²-(9x²-6)]/[3x+√(9x²-6)]
x→+∞
=lim(9x²-9x²+6)/[3x+√(9x²-6)]
x→+∞
=lim 6/[3x+√(9x²-6)]
x→+∞
=lim (6/x)/[3+√(9- 6/x²)]
x→+∞
=0/[3+√(9-0)]
=0/(3+3)
=0/6
=0
lim[3x-√(9x²-6)]
x→+∞
=lim[3x-√(9x²-6)][3x+√(9x²-6)]/[3x+√(9x²-6)]
x→+∞
=lim[(3x)²-(9x²-6)]/[3x+√(9x²-6)]
x→+∞
=lim(9x²-9x²+6)/[3x+√(9x²-6)]
x→+∞
=lim 6/[3x+√(9x²-6)]
x→+∞
=lim (6/x)/[3+√(9- 6/x²)]
x→+∞
=0/[3+√(9-0)]
=0/(3+3)
=0/6
=0
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