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

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

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

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

e^{\frac{1}{y}}

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{\frac{1}{y}}

= e^{\frac{1}{y}}

\int (2 + \frac{1}{x})^{2} d x

n = 1 \sum \infty (\frac{2}{5})^{n}

\frac{sin ( x ^{2} )}{3 x}

\frac{1 + x}{1 - x}

n = 0 \sum \infty \frac{1}{e ^{2 n}}

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