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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = 3

\int_{0}^{2} 5 d x

\frac{\partial}{\partial x} (x y^{9} - x^{2} y)

x \to 6 lim (x^{2} + 13)

\frac{d y}{d x} = 2 x y^{4}

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