What is the limit as x approaches 0 of (4x+1)^{1/x} ?

The limit as x approaches 0 of (4x+1)^{1/x} is e^4

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limit as x approaches 0 of (4x+1)^{1/x}

x \to 0 lim ((4 x + 1)^{\frac{1}{x}})

e^{4}

Decimal

54.59815 \dots

Solution steps

x \to 0 lim ((4 x + 1)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (4 x + 1)})

Apply the Limit Chain Rule:

e^{4}

= e^{4}

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

x \to 0 lim (x [x] cot (x))

b \to \infty lim (e^{- b})

x \to 0 lim (x^{e^{x} - 1})

x \to - \infty lim (7^{x})

What is the limit as x approaches 0 of (4x+1)^{1/x} ?
The limit as x approaches 0 of (4x+1)^{1/x} is e^4