What is the limit as x approaches infinity of (1+2/(x+1))^{x+1} ?

The limit as x approaches infinity of (1+2/(x+1))^{x+1} is e^2

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limit as x approaches infinity of (1+2/(x+1))^{x+1}

x \to \infty lim ((1 + \frac{2}{x + 1})^{x + 1})

e^{2}

Decimal Notation

7.38905 \dots

Solution steps

x \to \infty lim ((1 + \frac{2}{x + 1})^{x + 1})

Apply exponent rules

= x \to \infty lim (e^{(x + 1) l n (1 + \frac{2}{x + 1})})

Apply the Limit Chain Rule:

e^{2}

= e^{2}

n = 0 \sum \infty n^{- 0.48}

x \to 1 lim ([f (x) + g (x)])

\frac{d}{d x} ((10 x)^{l n (10 x)})

\frac{\partial}{\partial x} (tan (x - y))

\int ln (1) d x

What is the limit as x approaches infinity of (1+2/(x+1))^{x+1} ?
The limit as x approaches infinity of (1+2/(x+1))^{x+1} is e^2