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

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

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

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

e^{10}

Decimal

22026.46579 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{10}

= e^{10}

2 x^{3} + 2 x y + 2 y^{2} = 38, (- 1, - 4)

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

\int_{2}^{5} \frac{1}{x - 2} d x

f (x) = (2 x^{3} + 5 x) (x - 3) (x + 2)

x \to π lim (3 cot (x))

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