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

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

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

x \to 0 + lim ((1 + \frac{6}{x})^{2 x})

1

Solution steps

x \to 0 + lim ((1 + \frac{6}{x})^{2 x})

Apply exponent rules

= x \to 0 + lim (e^{2 x l n (1 + \frac{6}{x})})

Apply the Limit Chain Rule:

1

= 1

x \to 8 lim (\frac{2}{x - 8})

x \to 0 + lim ((5 x)^{6 x})

x \to 5 lim (\frac{5 x}{5 - x})

x \to 0 + lim (x^{12 x})

x \to π lim (tan (\frac{3 x}{4}))

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