Final answer to the problem
Step-by-step Solution
Specify the solving method
Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
Learn how to solve limits to infinity problems step by step online.
$\lim_{x\to\infty }\left(e^{x\ln\left(1+\frac{-1}{x^2}\right)}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of (1+-1/(x^2))^x 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. Evaluate the limit \lim_{x\to\infty }\left(x\ln\left(1+\frac{-1}{x^2}\right)\right) by replacing all occurrences of x by \infty .