Indeterminate forms
Limits and continuity · Mathematics
Study notes
Q: Evaluate: (a) lim(x→∞) (√(x²+1) − x) (b) lim(x→0⁺) x·lnx. (a) ∞−∞: multiply conjugate: 1/(√(x²+1)+x) → 0. (b) 0·(−∞): rewrite as lnx/(1/x), then L'Hôpital: (1/x)/(−1/x²) = −x → 0.