(4)
lim [√(x²+1)-√(x²-1)]
x→∞
=lim [√(x²+1)-√(x²-1)][√(x²+1)+√(x²-1)]/[√(x²+1)+√(x²-1)]
x→∞
=lim [(x²+1)-(x²-1)]/[√(x²+1)+√(x²-1)]
x→∞
=lim 2/[√(x²+1)+√(x²-1)]
x→∞
=lim (2/|x|)/[√(1+ 1/x²)+√(1- 1/x²)]
x→∞
=0/[√(1+0)+√(1-0)]
=0/2
=0
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