Find the limit of $\ln\left(1+e^{\left(\sqrt{1+ax^2}\right)}\right)$ as $x$ approaches $\infty $

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Learn how to solve limits by rationalizing problems step by step online. Find the limit of ln(1+e^(1+ax^2)^(1/2)) as x approaches infinity. The limit of a logarithm is equal to the logarithm of the limit. Applying rationalisation. Multiply and simplify the expression within the limit. Simplify \left(e^{\left(\sqrt{1+ax^2}\right)}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \sqrt{1+ax^2} and n equals 2.