What is the limit as x approaches 0+of (1+3x)^{1/x} ?

The limit as x approaches 0+of (1+3x)^{1/x} is e^3

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limit as x approaches 0+of (1+3x)^{1/x}

x \to 0 + lim ((1 + 3 x)^{\frac{1}{x}})

e^{3}

Decimal

20.08553 \dots

Solution steps

x \to 0 + lim ((1 + 3 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{1}{x} l n (1 + 3 x)})

Apply the Limit Chain Rule:

e^{3}

= e^{3}

\frac{\partial}{\partial x} (- y - \frac{2 x}{y ^{3}})

\int \frac{ln ( x + 1 )}{( x + 1 )} d x

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

\frac{1}{s ^{2} + 6 s + 34}

1 - e^{- t}

What is the limit as x approaches 0+of (1+3x)^{1/x} ?
The limit as x approaches 0+of (1+3x)^{1/x} is e^3