Final answer to the problem
$\frac{1}{e}$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
- Load more...
Can't find a method? Tell us so we can add it.
1
Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
$\lim_{x\to1}\left(e^{\frac{1}{1-x}\ln\left(x\right)}\right)$
Learn how to solve limits of exponential functions problems step by step online.
$\lim_{x\to1}\left(e^{\frac{1}{1-x}\ln\left(x\right)}\right)$
Learn how to solve limits of exponential functions problems step by step online. Find the limit of x^(1/(1-x)) as x approaches 1. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(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
$\frac{1}{e}$
Exact Numeric Answer
$0.3678794$
