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- Solve using L'Hôpital's rule
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- Integrate by partial fractions
- Product of Binomials with Common Term
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As it's an indeterminate limit of type $\frac{\infty}{\infty}$, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is
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$\lim_{x\to\infty }\left(\left(\frac{\frac{x-1}{x}}{\frac{x+1}{x}}\right)^x\right)$
Learn how to solve problems step by step online. Find the limit of ((x-1)/(x+1))^x as x approaches infinity. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Separate the terms of both fractions. Simplify the fraction . The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}.
