What is the limit as x approaches 0+of tan(x^x) ?

The limit as x approaches 0+of tan(x^x) is tan(1)

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limit as x approaches 0+of tan(x^x)

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

tan (1)

Decimal

1.55740 \dots

Solution steps

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

Apply the Limit Chain Rule:

tan (1)

= tan (1)

x \to 1 lim ((x^{2} - 4) (x - 3))

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

x \to 0 + lim (\frac{1 - cos ( x )}{x ( 1 - cos ( x ) )})

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

x \to 0 lim (ln (x + 1))

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