Step-by-step Solution

Find the limit $\lim_{x\to\infty }\left(\left(1-\left(\frac{1}{x}\right)\right)^x\right)$

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Step-by-step Solution

Problem to solve:

$\lim_{x\to\infty}\left(1-\frac{1}{x}\right)^x$

Solving method

Learn how to solve limits to infinity problems step by step online.

$\lim_{x\to\infty }\left(\left(1+\frac{-1}{x}\right)^x\right)$

Unlock this full step-by-step solution!

Learn how to solve limits to infinity problems step by step online. Find the limit (x)->(\infty)lim((1-1/x)^x). Multiplying the fraction by -1. 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.

Final Answer

$\frac{1}{e}$$\,\,\left(\approx 0.36787944117144233\right)$