What is the limit as x approaches 0 of (1-x/2)^{5/x} ?

The limit as x approaches 0 of (1-x/2)^{5/x} is 1/(e^{5/2)}

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limit as x approaches 0 of (1-x/2)^{5/x}

x \to 0 lim ((1 - \frac{x}{2})^{\frac{5}{x}})

\frac{1}{e ^{\frac{5}{2}}}

Decimal Notation

0.08208 \dots

Solution steps

x \to 0 lim ((1 - \frac{x}{2})^{\frac{5}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (1 - \frac{x}{2})})

Apply the Limit Chain Rule:

\frac{1}{e ^{\frac{5}{2}}}

= \frac{1}{e ^{\frac{5}{2}}}

x \to 0 - lim (1 - 4 x)

x \to 1 lim (\frac{1}{( x - 1 ) ^{4} + 2})

x \to 0 lim (\frac{( 5 ^{x} - 4 ^{x} )}{x})

x \to 0 lim (cos (\frac{2 π}{x}))

What is the limit as x approaches 0 of (1-x/2)^{5/x} ?
The limit as x approaches 0 of (1-x/2)^{5/x} is 1/(e^{5/2)}