limx→∞,[√(x^2 + 1)-√(x^2 - 1)]
=limx→∞,[x^2 + 1)-(x^2 - 1)]/[√(x^2 + 1)+√(x^2 - 1)]
=limx→∞,2/[√(x^2 + 1)+√(x^2 - 1)]
=limx→∞,2/(x+x)
=limx→∞,1/x
=0
limx→∞,[√(x^2 + 1)-√(x^2 - 1)]
=limx→∞,[x^2 + 1)-(x^2 - 1)]/[√(x^2 + 1)+√(x^2 - 1)]
=limx→∞,2/[√(x^2 + 1)+√(x^2 - 1)]
=limx→∞,2/(x+x)
=limx→∞,1/x
=0