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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int (\frac{x}{x - 1}) d x

x \to θ lim (x^{2} - 5)

\int \frac{x}{3 + x ^{2}} d x

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

x \to 0 lim (tan (x) - sin (x))

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