Final answer to the problem
Step-by-step Solution
Specify the solving method
Apply the power rule of limits: $\displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}$
Learn how to solve limits to infinity problems step by step online.
${\left(\lim_{x\to\infty }\left(e\right)\right)}^{\lim_{x\to\infty }\left(-x\right)}$
Learn how to solve limits to infinity problems step by step online. Find the limit of e^(-x) as x approaches infinity. 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. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. Evaluate the limit \lim_{x\to\infty }\left(x\right) by replacing all occurrences of x by \infty .