Final answer to the problem
$\ln\left(c-f\right)$
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Step-by-step Solution
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- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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1
The limit of a logarithm is equal to the logarithm of the limit
$\ln\left(\lim_{x\to\infty }\left(1+e^{\left(\sqrt{1+ax^2}\right)}\right)\right)$
Learn how to solve limits by rationalizing problems step by step online.
$\ln\left(\lim_{x\to\infty }\left(1+e^{\left(\sqrt{1+ax^2}\right)}\right)\right)$
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.
Final answer to the problem
$\ln\left(c-f\right)$
