i)
lim (x → ∞) = (2x² + 4) / (x² - 1)
lim (x → ∞) = (2 + 4/x^2) / (1 - 1/x^2) = 2/1 =2
ii)
lim (x → 1) = (x - 1) / (x² - 1)
lim (x → 1) = (x - 1) / ((x + 1)(x - 1))
lim (x → 1) = 1 / (x + 1) = 1/2
iii)
lim (x → 0) = (√(x + 1) - 1) / x
L'Hospital
lim (x → 0) = 1/(2·√(x + 1)) = 1/2