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

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

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

x \to 0 + lim (x^{t a n (x)})

1

Solution steps

x \to 0 + lim (x^{t a n (x)})

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int ((ln (x))^{2}) d x

4 x^{2} tan (x)

\frac{\partial}{\partial x} (x e x p (x, y, z) (- x^{2} - y^{2} - z^{2}))

f (x) = - 4 sin (x), at x = π

\int \frac{sech ^{2} ( x )}{tanh ( x )} d x

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