Limits : getting number $e$

Calculus Level 2

Which of the following limits is equal to $e?$

Clarification: $e \approx 2.71828$ denotes the Euler's number .

\displaystyle \lim _ { x \to - \infty } \left ( x + \frac { 1 } { x } \right ) ^ { x }

\displaystyle \lim _ { x \to 0 } \left ( 1 + \frac { 1 } { x } \right ) ^ { x }

\displaystyle \lim _ { x \to 0 } \left ( x - \frac { 1 } { x } \right ) ^ { x }

\displaystyle \lim _ { x \to \infty } \left ( x + \frac { 1 } { x } \right ) ^ { x }

\displaystyle \lim _ { x \to 0 } \left ( x + \frac { 1 } { x } \right ) ^ { x }

\displaystyle \lim _ { x \to \infty } \left ( 1 + \frac { 1 } { x } \right ) ^ { x }

\displaystyle \lim _ { x \to - \infty } \left ( 1 + \frac { 1 } { x } \right ) ^ { x }

\displaystyle \lim _ { x \to 0 } \left ( 1 - \frac { 1 } { x } \right ) ^ { x }

1 solution

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Apr 6, 2021

See e .