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
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- 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: $a^x=e^{x\ln\left(a\right)}$
$\lim_{x\to\infty }\left(e^{\left(x+1\right)\ln\left(\frac{x+2}{x}\right)}\right)$
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$\lim_{x\to\infty }\left(e^{\left(x+1\right)\ln\left(\frac{x+2}{x}\right)}\right)$
Learn how to solve problems step by step online. Find the limit of ((x+2)/x)^(x+1) as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\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. Rewrite the product inside the limit as a fraction.
Final answer to the problem
$e^{2}$
Exact Numeric Answer
$7.3890561$
