Mathematics

This limit has the indeterminate form $1^{\infty}$, which signals an exponential growth problem. The key insight is to use logarithms: take $\ln$ of the expression, find that limit first, then exponentiate back. You'll recognize the result as a close cousin of the famous limit $\lim_{u\to 0}(1+u)^{1/u} = e$.

This limit has the indeterminate form $1^{\infty}$, which signals an exponential growth problem. The key insight is to use logarithms: take $\ln$ of the expression, find that limit first, then exponentiate back. You'll recognize the result as a close cousin of the famous limit $\lim_{u\to 0}(1+u)^{1/u} = e$.