What is the limit as x approaches 0 of (1+3x)^{5/x} ?

The limit as x approaches 0 of (1+3x)^{5/x} is e^{15}

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limit as x approaches 0 of (1+3x)^{5/x}

x \to 0 lim ((1 + 3 x)^{\frac{5}{x}})

e^{15}

Solution steps

x \to 0 lim ((1 + 3 x)^{\frac{5}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (1 + 3 x)})

Apply the Limit Chain Rule:

e^{15}

= e^{15}

\int 5 x e^{6 x} d x

(e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x} - \frac{5 e ^{\frac{1}{x}}}{x ^{2}})^{^{'}}

t \to 0 lim ((t - 2)^{5})

\frac{( x - 1 )}{( x + 2 )}

y^{^{'}} = \frac{4 x ln ( 2 x )}{sin ( y )}

What is the limit as x approaches 0 of (1+3x)^{5/x} ?
The limit as x approaches 0 of (1+3x)^{5/x} is e^{15}