What is the limit as x approaches 0 of (3x+1)^{2/x} ?

The limit as x approaches 0 of (3x+1)^{2/x} is e^6

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limit as x approaches 0 of (3x+1)^{2/x}

x \to 0 lim ((3 x + 1)^{\frac{2}{x}})

e^{6}

Decimal Notation

403.42879 \dots

Solution steps

x \to 0 lim ((3 x + 1)^{\frac{2}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{2}{x} l n (3 x + 1)})

Apply the Limit Chain Rule:

e^{6}

= e^{6}

x \to 0 lim (coth (\frac{1}{x}))

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

x \to 0 + lim ((- 2 ln (x))^{x})

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

x \to 0 lim (\frac{ln ( x ^{4} )}{x})

What is the limit as x approaches 0 of (3x+1)^{2/x} ?
The limit as x approaches 0 of (3x+1)^{2/x} is e^6