Limit
lim [x→∞] √(ax² + bx + c) - √(px² + qx + r) = (b - q)/2√a
••
lim x→∞ (x - √(x² - 5x + 3))
= lim x→∞ (√(x² + 0x + 0) - √(x² - 5x + 3))
= (0 - (-5))/2√1
= 5/2
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Limit
lim [x→∞] √(ax² + bx + c) - √(px² + qx + r) = (b - q)/2√a
••
lim x→∞ (x - √(x² - 5x + 3))
= lim x→∞ (√(x² + 0x + 0) - √(x² - 5x + 3))
= (0 - (-5))/2√1
= 5/2