The value of the following limit is _____________.

Answer: -1/2

• Substitute u = √x. As x → 0+, we have u → 0+, and the limit becomes u / (1 - e^{2u}).

• Rewrite the denominator: 1 - e^{2u} = - (e^{2u} - 1), so the expression equals - u / (e^{2u} - 1).

• Use the expansion e^{2u} - 1 = 2u + o(u) as u → 0, hence u / (e^{2u} - 1) → 1/2. Therefore the original limit equals -1/2.