lim_{x - 0} (sqrt(x + 1) - 1) / x = ______

(Round off to one decimal place)

Question

lim_{x -> 0} (sqrt(x + 1) - 1) / x = ______

(Round off to one decimal place)

Accepted Answer

0.5 This limit has the 0/0 indeterminate form at x = 0. We can resolve it by rationalizing the numerator (multiplying by the conjugate) or applying L'Hopital's rule. Both methods quickly yield 1/2 = 0.5.