What is the limit as h approaches 0 of (1+5h)^{1/h} ?

The limit as h approaches 0 of (1+5h)^{1/h} is e^5

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limit as h approaches 0 of (1+5h)^{1/h}

h \to 0 lim ((1 + 5 h)^{\frac{1}{h}})

e^{5}

Decimal Notation

148.41315 \dots

Solution steps

h \to 0 lim ((1 + 5 h)^{\frac{1}{h}})

Apply exponent rules

= h \to 0 lim (e^{\frac{1}{h} l n (1 + 5 h)})

Apply the Limit Chain Rule:

e^{5}

= e^{5}

\frac{d}{d x} (y^{2} - x^{2})

\int e^{5 x + e^{5 x}} d x

\frac{s}{2 s ^{2} + 4 s + 3}

\frac{d y}{d x} = \frac{x 1 - y ^{2}}{y 1 - x ^{2}}

\int x^{3} - 2 x^{- 2} + 6 x d x

What is the limit as h approaches 0 of (1+5h)^{1/h} ?
The limit as h approaches 0 of (1+5h)^{1/h} is e^5