Final answer to the problem
$e^{2}$
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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
Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
Learn how to solve limits by l'hôpital's rule problems step by step online.
$\lim_{x\to0}\left(e^{\frac{1}{x}\ln\left(e^x+x\right)}\right)$
Learn how to solve limits by l'hôpital's rule problems step by step online. Find the limit of (e^x+x)^(1/x) as x approaches 0. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(e^x+x\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.
Final answer to the problem
$e^{2}$
Exact Numeric Answer
$7.3890561$
