Lim x->0 1-cos8x / 3x^2

Lim x-> бесконечность (x-1 / x) ^2-3x

Limx->бесконечность (2x+3 / 5x+7) ^x+1

X→0; cosx→ 1 - x²/2 ⇒

lim x→0 (1 - cos8x) / 3x² = lim (1-1 + (8x) ²/3x² = lim (64x²/2) / 3x² =

= 32/3 = 10' 2/3

lim n→∞ (1+1/n) ^n = e

lim x→∞ (1 - 1/x) ^ (2-3x) = { lim (1-1/y) ^2] / {[lim (1-1/x) ^x]³ =

= 1 / (1/e) ³ = e3

lim x→∞ [ (2+3/x) / (5+7/x) ]^ (x+1) = 2/5