What is the limit as x approaches infinity of (1+1/x)^{x+3} ?

The limit as x approaches infinity of (1+1/x)^{x+3} is e

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limit as x approaches infinity of (1+1/x)^{x+3}

x \to \infty lim ((1 + \frac{1}{x})^{x + 3})

e

Decimal

2.71828 \dots

Solution steps

x \to \infty lim ((1 + \frac{1}{x})^{x + 3})

Simplify

(1 + \frac{1}{x})^{x + 3} : (1 + \frac{1}{x})^{x} (1 + \frac{1}{x})^{3}

= x \to \infty lim ((1 + \frac{1}{x})^{x} (1 + \frac{1}{x})^{3})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim ((1 + \frac{1}{x})^{x}) \cdot x \to \infty lim ((1 + \frac{1}{x})^{3})

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

x \to \infty lim ((1 + \frac{1}{x})^{3}) = 1

= e 1

Simplify

= e

y^{^{''}} = - k y

- sin (x^{2}) (2 x)

\int 2 e^{3 t} d t

\int_{0}^{3} 1 + 4 x^{2} d x

f (x) = 2 x^{3} - 6 x^{2} - 90 x - 1

What is the limit as x approaches infinity of (1+1/x)^{x+3} ?
The limit as x approaches infinity of (1+1/x)^{x+3} is e