<Li> lim x → 0 sin ⁡ x x = 1 (\ displaystyle \ lim _ (x \ to 0) (\ frac (\ sin x) (x)) = 1) </Li> <Li> lim x → 0 1 − cos ⁡ x x = 0 (\ displaystyle \ lim _ (x \ to 0) (\ frac (1 - \ cos x) (x)) = 0) </Li> <Li> lim x → ∞ x sin ⁡ (1 x) = 1 (\ displaystyle \ lim _ (x \ to \ infty) x \ sin \ left ((\ frac (1) (x)) \ right) = 1) </Li> <Ul> <Li> lim x → 0 (1 + x) 1 x = lim r → ∞ (1 + 1 r) r = e (\ displaystyle \ lim _ (x \ to 0) (1 + x) ^ (\ frac (1) (x)) = \ lim _ (r \ to \ infty) \ left (1 + (\ frac (1) (r)) \ right) ^ (r) = e) </Li> <Li> lim x → 0 e x − 1 x = 1 (\ displaystyle \ lim _ (x \ to 0) (\ frac (e ^ (x) - 1) (x)) = 1) </Li> <Li> lim x → 0 e a x − 1 b x = a b (\ displaystyle \ lim _ (x \ to 0) (\ frac (e ^ (ax) - 1) (bx)) = (\ frac (a) (b))) </Li> <Li> lim x → 0 c a x − 1 b x = a b ln ⁡ c (\ displaystyle \ lim _ (x \ to 0) (\ frac (c ^ (ax) - 1) (bx)) = (\ frac (a) (b)) \ ln c) </Li> <Li> lim x → 0 + x x = 1 (\ displaystyle \ lim _ (x \ to 0 ^ (+)) x ^ (x) = 1) </Li> </Ul>

Rules used to limit the volume of log information