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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to - 3 + lim (x^{2} - 9)

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

x \to \frac{π}{2} + lim (x^{2} tan (x))

x \to \infty lim (\frac{5}{2})

x \to 4 lim (\frac{6 - x + 32}{x - 2})

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