What is the limit as x approaches 0+of x^{pix} ?

The limit as x approaches 0+of x^{pix} is 1

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limit as x approaches 0+of x^{pix}

x \to 0 + lim (x^{π x})

1

Solution steps

x \to 0 + lim (x^{π x})

Apply exponent rules

= x \to 0 + lim (e^{π x l n (x)})

Apply the Limit Chain Rule:

1

= 1

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

x \to 4 lim (x^{2} + 5 x - 35)

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

x \to 0 + lim (x ln (tan (x)))

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

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