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

The limit as x approaches 0+of (1+5x)^{2/x} is e^{10}

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

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

e^{10}

Decimal

22026.46579 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{10}

= e^{10}

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

x \to 1 lim (\frac{3 x}{x - 1})

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

x \to \infty lim (\frac{30}{x})

x \to 0 - lim (\frac{x ^{3} + 4}{x ^{2}})

What is the limit as x approaches 0+of (1+5x)^{2/x} ?
The limit as x approaches 0+of (1+5x)^{2/x} is e^{10}