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

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

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

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

e^{\frac{1}{x}}

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{\frac{1}{x}}

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

\frac{d}{d x} (6 x^{- \frac{5}{6}})

\frac{\partial}{\partial x} (5 x + 2 y)

x \to 0 lim (x^{- 5})

d er i v a t i v e \frac{1}{2 x} - \frac{5}{2 x ^{\frac{3}{2}}}

d er i v a t i v e f (x) = \frac{x}{x + \frac{a}{x}}

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