Learn how to solve differential equations problems step by step online. Find the limit of (2+(x^2)/2)^(1/ln(2x)) as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(2+\frac{x^2}{2}\right). Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant.

Find the limit of (2+(x^2)/2)^(1/ln(2x)) as x approaches infinity