What is the limit as x approaches 0 of (1+x)^{4/x} ?

The limit as x approaches 0 of (1+x)^{4/x} is e^4

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limit as x approaches 0 of (1+x)^{4/x}

x \to 0 lim ((1 + x)^{\frac{4}{x}})

e^{4}

Decimal Notation

54.59815 \dots

Solution steps

x \to 0 lim ((1 + x)^{\frac{4}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{4}{x} l n (1 + x)})

Apply the Limit Chain Rule:

e^{4}

= e^{4}

x^{2} y^{^{''}} + x y^{^{'}} + 4 y = 0

\frac{\partial}{\partial y} (3 x^{2} + y)

\int (sec^{3} (x)) d x

f (x) = x^{2} - 5 x + 5, (0, 5)

\frac{d}{d t} (e^{t} (cos (t)))

What is the limit as x approaches 0 of (1+x)^{4/x} ?
The limit as x approaches 0 of (1+x)^{4/x} is e^4